Publications

Books:

K. Burnecki. Identification, validation and prediction of fractional dynamical systems", Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław (2012).

Articles and book chapters:

	W. Wang, M. Balcerek, K. Burnecki, A. Chechkin, S. Janušonis, J. Ślęzak, T. Vojta, A. Wyłomańska, and R. Metzler. Memory-multi-fractional Brownian motion with continuous correlations. Physical Review Research, 5(3):1-8, 2023. [ bib \| DOI \| http ]
	M. Balcerek, K. Burnecki, S. Thapa, A. Wyłomańska, and A. Chechkin. Fractional Brownian motion with random Hurst exponent: Accelerating diffusion and persistence transitions. Chaos, 32(9):1-16, 2022. [ bib \| DOI ]
	K. Burnecki, M. A. Teuerle, and A. Wilkowska. Diffusion approximations of the ruin probability for the insurer-reinsurer model driven by a renewal process. Risks, 10(6):1-16, 2022. [ bib \| DOI \| http ]
	F. Sabzikar, J. S. Kabala, and K. Burnecki. Tempered fractionally integrated process with stable noise as a transient anomalous diffusion model. Journal of Physics. A, Mathematical and Theoretical, 55(17):1-27, 2022. [ bib \| DOI \| http ]
	J. B. Janczura, K. Burnecki, M. Muszkieta, A. Stanislavsky, and A. Weron. Classification of random trajectories based on the fractional Lévy stable motion. Chaos, Solitons and Fractals, 154:1-9, 2022. [ bib \| DOI \| http ]
	J. S. Kabala, K. Burnecki, and F. Sabzikar. Tempered linear and non-linear time series models and their application to heavy-tailed solar flare data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(11):113124, 2021. [ bib \| DOI \| arXiv \| www: ]
	M. Balcerek, K. Burnecki, G. Sikora, and A. Wyłomańska. Discriminating Gaussian processes via quadratic form statistics. Chaos, 31(6):1-16, 2021. [ bib \| DOI \| http ]
	J. B. Janczura, M. Balcerek, K. Burnecki, A. Sabri, M. Weiß, and D. Krapf. Identifying heterogeneous diffusion states in the cytoplasm by a hidden Markov model. New Journal of Physics, 23:1-11, 2021. [ bib \| DOI \| http ]
	K. Burnecki, M. A. Teuerle, and A. Wilkowska. Ruin probability for the insurer-reinsurer model for exponential claims: a probabilistic approach. Risks, 9(5):1-10, 2021. [ bib \| DOI \| http ]
	M. Balcerek and K. Burnecki. Testing of multifractional Brownian motion. Entropy, 22(12):1-17, 2020. [ bib \| DOI ]
	A. Stanislavsky, W. Nitka, M. Małek, K. Burnecki, and J. B. Janczura. Prediction performance of Hidden Markov modelling for solar flares. Journal of Atmospheric and Solar-Terrestrial Physics, 208:1-7, 2020. [ bib \| DOI \| http ]
	A. Wyłomańska, D. R. Iskander, and K. Burnecki. Omnibus test for normality based on the edgeworth expansion. PLoS ONE, 15(6):1-36, 2020. [ bib \| DOI \| http ]
	M. Balcerek and K. Burnecki. Testing of fractional Brownian motion in a noisy environment. Chaos, Solitons and Fractals, 140:1-7, 2020. [ bib \| DOI ]
	W. Nitka and K. Burnecki. Impact of solar activity on precipitation in the United States. Physica. A, Statistical Mechanics and its Applications, 527:1-10, 2019. [ bib \| DOI \| http ]
	K. Burnecki, M. N. Giuricich, and Z. Palmowski. Valuation of contingent convertible catastrophe bonds - the case for equity conversion. Insurance. Mathematics and Economics, 88:238-254, 2019. [ bib \| DOI \| http ]
	J. Ślęzak, K. Burnecki, and R. Metzler. Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems. New Journal of Physics, 21:1-18, 2019. [ bib \| DOI ]
	K. Burnecki, M. A. Teuerle, and A. Wilkowska. De Vylder type approximation of the ruin probability for the insurer-reinsurer model. Mathematica Applicanda, 47(1):5-24, 2019. [ bib \| DOI \| http ]
	M. N. Giuricich and K. Burnecki. Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing. Physica. A, Statistical Mechanics and its Applications, 525(1):498-513, 2019. [ bib \| DOI \| http ]
	A. Stanislavsky, K. Burnecki, J. B. Janczura, K. Niczyj, and A. Weron. Solar X-ray variability in terms of a fractional heteroskedastic time series model. Monthly Notices of the Royal Astronomical Society, 485(3):3970–3980, 2019. [ bib \| DOI \| http ]
	M. Balcerek, H. Loch-Olszewska, J. A. Torrena-Pina, M. F. Garcia-Parajo, A. Weron, C. Manzo, and K. Burnecki. Inhomogeneous membrane receptor diffusion explained by a fractional heteroscedastic time series model. Physical Chemistry Chemical Physics, 21(6):3114-3121, 2019. [ bib \| DOI \| http ]
	K. Burnecki, G. Sikora, A. Weron, M. M. Tamkun, and D. Krapf. Identifying diffusive motions in single-particle trajectories on the plasma membrane via fractional time-series models. Physical Review E, 99(1):1-10, 2019. [ bib \| DOI \| http ]
	J. R. Gajda, G. Bartnicki, and K. Burnecki. Modeling of water usage by means of ARFIMA-GARCH processes. Physica. A, Statistical Mechanics and its Applications, 512:644-657, 2018. [ bib \| DOI \| http ]
	K. Burnecki and M. N. Giuricich. Stable weak approximation at work in index-linked catastrophe bond pricing. Risks, 5(4):1-19, 2017. [ bib \| DOI ]
	K. Burnecki and G. Sikora. Identification and validation of stable ARFIMA processes with application to UMTS data. Chaos, Solitons and Fractals, 102:456-466, 2017. [ bib \| DOI ]
	T. Sungkaworn, M.-L. Jobin, K. Burnecki, A. Weron, M. J. Lohse, and D. Calebiro. Single-molecule imaging reveals receptor-G protein interactions at cell surface hot spots. Nature, 550(7677):543-547, 2017. [ bib \| DOI ]
	G. Sikora, E. Kepten, A. Weron, M. Balcerek, and K. Burnecki. An efficient algorithm for extracting the magnitude of the measurement error for fractional dynamics. Physical Chemistry Chemical Physics, 19(39):26566-26581, 2017. [ bib \| DOI ]
	A. Weron, K. Burnecki, E. J. Akin, L. Sole, M. Balcerek, M. M. Tamkun, and D. Krapf. Ergodicity breaking on the neuronal surface emerges from random switching between diffusive states. Scientific Reports, 7:1-10, 2017. [ bib \| DOI ]
	G. Sikora, K. Burnecki, and A. Wyłomańska. Mean-squared-displacement statistical test for fractional Brownian motion. Physical Review E, 95(3):1-5, 2017. [ bib \| DOI ]
	K. Burnecki, A. Wyłomańska, and A. Chechkin. Discriminating between light- and heavy-tailed distributions with limit theorem. PLoS ONE, 10(12):1-23, 2015. [ bib \| DOI ]
	E. Kepten, A. Weron, I. Bronshtein, K. Burnecki, and Y. Garini. Uniform contraction-expansion description of relative centromere and telomere motion. Biophysical Journal, 109(10):1454 - 1462, 2015. [ bib \| DOI ]
	K. Burnecki, E. Kepten, Y. Garini, G. Sikora, and A. Weron. Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors - an alternative approach. Scientific Reports, 5:1-11, 2015. [ bib \| DOI ]
	E. Kepten, A. Weron, G. Sikora, K. Burnecki, and Y. Garini. Guidelines for the fitting of anomalous diffusion mean square displacement graphs from single particle tracking experiments. PLoS ONE, 10(2):1-10, 2015. [ bib \| DOI ]
	K. Burnecki and A. Weron. Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling. Journal of Statistical Mechanics: Theory and Experiment, P10036(10):1-26, 2014. [ bib \| DOI ]
	K. Burnecki and G. Sikora. Estimation of FARIMA parameters in the case of negative memory and stable noise. IEEE Transactions on Signal Processing, 61(11):2825-2835, 2013. [ bib \| DOI ]
	K. Burnecki, E. Kepten, J. B. Janczura, I. Bronshtein, Y. Garini, and A. Weron. Universal algorithm for identification of fractional Brownian motion. a case of telomere subdiffusion. Biophysical Journal, 103(9):1839-1847, 2012. [ bib \| DOI ]
	K. Burnecki, G. Sikora, and A. Weron. Fractional process as a unified model for subdiffusive dynamics in experimental data. Physical Review. E, Statistical Nonlinear and Soft Matter Physics, 86(4):041912-1 - 041912-8, 2012. [ bib \| DOI ]
	K. Burnecki. FARIMA processes with application to biophysical data. Journal of Statistical Mechanics: Theory and Experiment, (5):P05015-1 - P05015-18, 2012. [ bib \| DOI ]
	K. Burnecki, A. Wyłomańska, A. Beletskii, V. Gonchar, and A. Chechkin. Recognition of stable distribution with Lévy index α close to 2. Physical Review. E, Statistical Nonlinear and Soft Matter Physics, 85(5):056711-1 - 056711-8, 2012. [ bib \| DOI ]
	P. Bieńkowski, K. Burnecki, J. B. Janczura, R. Weron, and B. Zubrzak. A new method for automated noise cancellation in electromagnetic field measurement. Journal of Electromagnetic Waves and Applications, 26(8/9):1226-1236, 2012. [ bib \| DOI ]
	K. Burnecki, M. Muszkieta, G. Sikora, and A. Weron. Statistical modelling of subdiffusive dynamics in the cytoplasm of living cells: a FARIMA approach. Europhysics Letters, 98(1):10004-p1 - 10004-p6, 2012. [ bib \| DOI ]
	K. Burnecki, M. Magdziarz, and A. Weron. Identification and validation of fractional subdiffusion dynamics. In J. Klafter, S. C. Lim, and R. Metzler, editors, Fractional dynamics: recent advances, pages 331-351. World Scientific, Singapore [i in.], 2012. [ bib \| DOI ]
	K. Burnecki, J. R. Gajda, and G. Sikora. Stability and lack of memory of the returns of the Hang Seng index. Physica. A, Statistical Mechanics and its Applications, 390(18/19):3136-3146, 2011. [ bib \| DOI ]
	K. Burnecki and M. A. Teuerle. Ruin probability in finite time. In P. Čižek, W. K. Härdle, and R. Weron, editors, Statistical tools for finance and insurance. 2nd Edition, pages 329-348. Springer, Berlin; Heidelberg, 2011. [ bib \| DOI ]
	K. Burnecki, J. B. Janczura, and R. Weron. Building loss models. In P. Čižek, W. K. Härdle, and R. Weron, editors, Statistical tools for finance and insurance. 2nd Edition, pages 293-328. Springer, Berlin; Heidelberg, 2011. [ bib \| DOI ]
	K. Burnecki and A. Weron. Fractional Lévy stable motion can model subdiffusive dynamics. Physical Review. E, Statistical Nonlinear and Soft Matter Physics, 82(2):021130-1 - 021130-8, 2010. [ bib \| DOI ]
	M. Magdziarz, A. Weron, K. Burnecki, and J. Klafter. Fractional Brownian motion versus the continuous-time random walk: A simple test for subdiffusive dynamics. Physical Review Letters, 103(18):180602-1 - 180602-4, 2009. [ bib \| DOI ]
	K. Burnecki, A. Stanislavsky, and K. Weron. Statistical analysis of the maximum energy in solar X-ray flare activity. Acta Physica Polonica B, 40(5):1303-1313, 2009. [ bib \| .pdf ]
	A. Stanislavsky, K. Burnecki, M. Magdziarz, A. Weron, and K. Weron. FARIMA modeling of solar flare activity from empirical time series of soft X-ray solar emission. Astrophysical Journal, 693(2):1877-1882, 2009. [ bib \| DOI ]
	K. Burnecki, J. Klafter, M. Magdziarz, and A. Weron. From solar flare time series to fractional dynamics. Physica. A, Statistical Mechanics and its Applications, 387(5/6):1077-1087, 2008. [ bib \| DOI ]
	K. Burnecki, J. B. Janczura, M. Magdziarz, and A. Weron. Can one see a competition between subdiffusion and Lévy flights? A case of geometric-stable noise. Acta Physica Polonica B, 39(5):1043-1053, 2008. [ bib \| .pdf ]
	K. Burnecki and R. Weron. Visualization tools for insurance risk processes. In Handbook of data visualization, pages 899-920. Springer, Berlin; Heidelberg, 2008. [ bib \| DOI ]
	K. Burnecki and J. Nowicka-Zagrajek. Składka kwantylowa w modelu ryzyka a dane szkodowe z obcięciem dolnym. In Statystyka aktuarialna - stan i perspektywy rozwoju w Polsce. Pod red. W. Ostasiewicza., volume nr 1108 of Prace Naukowe Akademii Ekonomicznej im. Oskara Langego we Wrocławiu, pages 306-317. Wydaw. AE, Wrocław, 2006. [ bib ]
	A. Chernobai, K. Burnecki, S. Rachev, S. Truck, and R. Weron. Modelling cathastrophe claims with left-truncated severity distributions. Computational Statistics, 21:537-555, 2006. [ bib \| DOI ]
	J. Nowicka-Zagrajek and K. Burnecki. Wybrane rodzaje składek w modelu ryzyka kolektywnego. In Inwestycje finansowe i ubezpieczenia - tendencje światowe a polski rynek. Red. nauk. Wanda Ronka-Chmielowiec, Krzysztof Jajuga. T. 2., volume nr 1088 of Prace Naukowe Akademii Ekonomicznej im. Oskara Langego we Wrocławiu, pages 48-55. Wydaw. AE, Wrocław, 2005. [ bib ]
	K. Burnecki, J. Nowicka-Zagrajek, and A. Wyłomańska. Pure risk premiums under deductibles. In Statistical tools for finance and insurance. [Eds] P. Čižek, W. Härdle, R. Weron., pages 427-452. Springer, Berlin, 2005. [ bib \| DOI ]
	K. Burnecki, P. Mista, and A. Weron. Ruin probabilities in finite and infinite time. In Statistical tools for finance and insurance. [Eds] P. Čižek, W. Härdle, R. Weron., pages 341-379. Springer, Berlin, 2005. [ bib \| DOI ]
	K. Burnecki and R. Weron. Modeling of the risk process. In Statistical tools for finance and insurance. [Eds] P. Čižek, W. Härdle, R. Weron., pages 319-339. Springer, Berlin, 2005. [ bib \| DOI ]
	K. Burnecki, A. Misiorek, and R. Weron. Loss distributions. In Statistical tools for finance and insurance. [Eds] P. Čižek, W. Härdle, R. Weron., pages 289-317. Springer, Berlin, 2005. [ bib \| DOI ]
	K. Burnecki, G. Kukla, and D. Taylor. Pricing of catastrophe bonds. In Statistical tools for finance and insurance. [Eds] P. Čižek, W. Härdle, R. Weron., pages 93-114. Springer, Berlin, 2005. [ bib \| DOI ]
	A. Weron, K. Burnecki, S. Mercik, and K. Weron. Complete description of all self-similar models driven by Lévy stable noise. Physical Review. E, Statistical Nonlinear and Soft Matter Physics, 71(1]):016113-1 - 016113-10, 2005. [ bib \| DOI ]
	K. Burnecki, W. Haerdle, and R. Weron. Simulation of risk processes. In J. L Teugels and B. Sundt, editors, Encyclopedia of actuarial science. Vol. 3, pages 1564-1570. Wiley, Chichester, 2004. [ bib ]
	K. Burnecki, P. Miśta, and A. Weron. What is the best approximation of ruin probability in infinite time? Applicationes Mathematicae, 32(2):155-176, 2005. [ bib ]
	K. Burnecki, P. Miśta, and A. Weron. A new gamma type approximation of the ruin probability. Acta Physica Polonica B, 36(5):1473-1483, 2005. [ bib \| .pdf ]
	K. Burnecki, A. Marciniuk, and A. Weron. On annuities under random rates of interest with payments varying in arithmetic and geometric progression. Probability and Mathematical Statistics, 24:1-15, 2004. [ bib \| .pdf ]
	K. Burnecki and A. Weron. Lévy stable processes. From stationary to self-similar dynamics and back. An application to finance. Acta Physica Polonica B, 35(4):1343-1358, 2004. [ bib \| .pdf ]
	K. Burnecki and G. Kukla. Pricing of zero-coupon and coupon cat bonds. Applicationes Mathematicae, 30(3):315-324, 2003. [ bib ]
	K. Burnecki, A. Marciniuk, and A. Weron. Annuities under random rates of interest - revisited. Insurance. Mathematics and Economics, 32(3):457-460, 2003. [ bib \| DOI ]
	S. Mercik, K. Weron, K. Burnecki, and A. Weron. Enigma of self-similarity of fractional Lévy stable motions. Acta Physica Polonica B, 34(7):3773-3791, 2003. [ bib \| .pdf ]
	K. Burnecki and G. Kukla. Obligacje katastroficzne. Krajobraz po wojnie. Asekuracja & Re, (1):29-30, 2003. [ bib ]
	K. Burnecki and Z. Michna. Simulation of Pickands constant. Probability and Mathematical Statistics, 22:193-199, 2002. [ bib \| .pdf ]
	K. Burnecki and G. Kukla. Instrumenty finansowe a ryzyko pogodowe. Asekuracja & Re, (10):26-27, 2001. [ bib ]
	K. Burnecki, J. Nowicka-Zagrajek, and A. Weron. Metoda pomiaru ryzyka (wartości zagrożonej - VaR) na rynku energii elektrycznej. Energetyka, (12):743-747, 2001. [ bib ]
	J. Nowicka-Zagrajek and K. Burnecki. Metody oceny ryzyka ubezpieczeniowego: Cz. 3. Estymacja parametrów rozkładu. Asekuracja & Re, (11):24-25, 2001. [ bib ]
	J. Nowicka-Zagrajek and K. Burnecki. Statystyczne metody oceny ryzyka ubezpieczeniowego: Cz. 2. Asekuracja & Re, (9):24-25, 2001. [ bib ]
	K. Burnecki and J. Nowicka-Zagrajek. Analiza umieralności. Asekuracja & Re, (7):29-30, 2001. [ bib ]
	J. Nowicka-Zagrajek and K. Burnecki. Statystyczne metody oceny ryzyka ubezpieczeniowego: Cz. 1. Asekuracja & Re, (5):20-21, 2001. [ bib ]
	J. Nowicka-Zagrajek and K. Burnecki. Tablice trwania życia. Asekuracja & Re, (4):24-25, 2001. [ bib ]
	K. Burnecki and J. Nowicka-Zagrajek. Czy straty mają ogony... czyli rozkłady żądań stosowane w matematyce ubezpieczeń majątkowych. Asekuracja & Re, (3):22-25, 2001. [ bib ]
	K. Burnecki. Self-similar processes as weak limits of a risk reserve process. Probability and Mathematical Statistics, 20:261-272, 2000. [ bib \| .pdf ]
	K. Burnecki and G. Kukla. Reasekuracja ryzyk ubezpieczeniowych na rynku kapitałowym. Obligacje katastroficzne. Rynek Terminowy, (4):128-134, 2000. [ bib ]
	K. Burnecki, G. Kukla, and R. Weron. Property insurance loss distributions. Physica. A, Statistical Mechanics and its Applications, 287(1/2):269-278, 2000. [ bib \| DOI ]
	K. Burnecki, J. Rosiński, and A. Weron. Spectral representation and structure of stable self-similar processes. In I. Karatzas, B. S. Rajput, and M. S. Taqqu, editors, Stochastic processes and related topics. In Memory of Stamatis Cambanis 1943-1995, Trends in Mathematics, pages 1-14. Birkhauser, Boston [i in.], 1998. [ bib \| DOI \| http ]
	K. Burnecki, M. Maejima, and A. Weron. The Lamperti transformation for self-similar processes. Yokohama Mathematical Journal, 44:25-42, 1997. [ bib ]

	W. Wang, M. Balcerek, K. Burnecki, A. Chechkin, S. Janušonis, J. Ślęzak, T. Vojta, A. Wyłomańska, and R. Metzler. Memory-multi-fractional Brownian motion with continuous correlations. Physical Review Research, 5(3):1-8, 2023. [ bib \| DOI \| http ]
	M. Balcerek, K. Burnecki, S. Thapa, A. Wyłomańska, and A. Chechkin. Fractional Brownian motion with random Hurst exponent: Accelerating diffusion and persistence transitions. Chaos, 32(9):1-16, 2022. [ bib \| DOI ]
	K. Burnecki, M. A. Teuerle, and A. Wilkowska. Diffusion approximations of the ruin probability for the insurer-reinsurer model driven by a renewal process. Risks, 10(6):1-16, 2022. [ bib \| DOI \| http ]
	F. Sabzikar, J. S. Kabala, and K. Burnecki. Tempered fractionally integrated process with stable noise as a transient anomalous diffusion model. Journal of Physics. A, Mathematical and Theoretical, 55(17):1-27, 2022. [ bib \| DOI \| http ]
	J. B. Janczura, K. Burnecki, M. Muszkieta, A. Stanislavsky, and A. Weron. Classification of random trajectories based on the fractional Lévy stable motion. Chaos, Solitons and Fractals, 154:1-9, 2022. [ bib \| DOI \| http ]
	J. S. Kabala, K. Burnecki, and F. Sabzikar. Tempered linear and non-linear time series models and their application to heavy-tailed solar flare data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(11):113124, 2021. [ bib \| DOI \| arXiv \| www: ]
	M. Balcerek, K. Burnecki, G. Sikora, and A. Wyłomańska. Discriminating Gaussian processes via quadratic form statistics. Chaos, 31(6):1-16, 2021. [ bib \| DOI \| http ]
	J. B. Janczura, M. Balcerek, K. Burnecki, A. Sabri, M. Weiß, and D. Krapf. Identifying heterogeneous diffusion states in the cytoplasm by a hidden Markov model. New Journal of Physics, 23:1-11, 2021. [ bib \| DOI \| http ]
	K. Burnecki, M. A. Teuerle, and A. Wilkowska. Ruin probability for the insurer-reinsurer model for exponential claims: a probabilistic approach. Risks, 9(5):1-10, 2021. [ bib \| DOI \| http ]
	M. Balcerek and K. Burnecki. Testing of multifractional Brownian motion. Entropy, 22(12):1-17, 2020. [ bib \| DOI ]
	A. Stanislavsky, W. Nitka, M. Małek, K. Burnecki, and J. B. Janczura. Prediction performance of Hidden Markov modelling for solar flares. Journal of Atmospheric and Solar-Terrestrial Physics, 208:1-7, 2020. [ bib \| DOI \| http ]
	A. Wyłomańska, D. R. Iskander, and K. Burnecki. Omnibus test for normality based on the edgeworth expansion. PLoS ONE, 15(6):1-36, 2020. [ bib \| DOI \| http ]
	M. Balcerek and K. Burnecki. Testing of fractional Brownian motion in a noisy environment. Chaos, Solitons and Fractals, 140:1-7, 2020. [ bib \| DOI ]
	W. Nitka and K. Burnecki. Impact of solar activity on precipitation in the United States. Physica. A, Statistical Mechanics and its Applications, 527:1-10, 2019. [ bib \| DOI \| http ]
	K. Burnecki, M. N. Giuricich, and Z. Palmowski. Valuation of contingent convertible catastrophe bonds - the case for equity conversion. Insurance. Mathematics and Economics, 88:238-254, 2019. [ bib \| DOI \| http ]
	J. Ślęzak, K. Burnecki, and R. Metzler. Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems. New Journal of Physics, 21:1-18, 2019. [ bib \| DOI ]
	K. Burnecki, M. A. Teuerle, and A. Wilkowska. De Vylder type approximation of the ruin probability for the insurer-reinsurer model. Mathematica Applicanda, 47(1):5-24, 2019. [ bib \| DOI \| http ]
	M. N. Giuricich and K. Burnecki. Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing. Physica. A, Statistical Mechanics and its Applications, 525(1):498-513, 2019. [ bib \| DOI \| http ]
	A. Stanislavsky, K. Burnecki, J. B. Janczura, K. Niczyj, and A. Weron. Solar X-ray variability in terms of a fractional heteroskedastic time series model. Monthly Notices of the Royal Astronomical Society, 485(3):3970–3980, 2019. [ bib \| DOI \| http ]
	M. Balcerek, H. Loch-Olszewska, J. A. Torrena-Pina, M. F. Garcia-Parajo, A. Weron, C. Manzo, and K. Burnecki. Inhomogeneous membrane receptor diffusion explained by a fractional heteroscedastic time series model. Physical Chemistry Chemical Physics, 21(6):3114-3121, 2019. [ bib \| DOI \| http ]
	K. Burnecki, G. Sikora, A. Weron, M. M. Tamkun, and D. Krapf. Identifying diffusive motions in single-particle trajectories on the plasma membrane via fractional time-series models. Physical Review E, 99(1):1-10, 2019. [ bib \| DOI \| http ]
	J. R. Gajda, G. Bartnicki, and K. Burnecki. Modeling of water usage by means of ARFIMA-GARCH processes. Physica. A, Statistical Mechanics and its Applications, 512:644-657, 2018. [ bib \| DOI \| http ]
	K. Burnecki and M. N. Giuricich. Stable weak approximation at work in index-linked catastrophe bond pricing. Risks, 5(4):1-19, 2017. [ bib \| DOI ]
	K. Burnecki and G. Sikora. Identification and validation of stable ARFIMA processes with application to UMTS data. Chaos, Solitons and Fractals, 102:456-466, 2017. [ bib \| DOI ]
	T. Sungkaworn, M.-L. Jobin, K. Burnecki, A. Weron, M. J. Lohse, and D. Calebiro. Single-molecule imaging reveals receptor-G protein interactions at cell surface hot spots. Nature, 550(7677):543-547, 2017. [ bib \| DOI ]
	G. Sikora, E. Kepten, A. Weron, M. Balcerek, and K. Burnecki. An efficient algorithm for extracting the magnitude of the measurement error for fractional dynamics. Physical Chemistry Chemical Physics, 19(39):26566-26581, 2017. [ bib \| DOI ]
	A. Weron, K. Burnecki, E. J. Akin, L. Sole, M. Balcerek, M. M. Tamkun, and D. Krapf. Ergodicity breaking on the neuronal surface emerges from random switching between diffusive states. Scientific Reports, 7:1-10, 2017. [ bib \| DOI ]
	G. Sikora, K. Burnecki, and A. Wyłomańska. Mean-squared-displacement statistical test for fractional Brownian motion. Physical Review E, 95(3):1-5, 2017. [ bib \| DOI ]
	K. Burnecki, A. Wyłomańska, and A. Chechkin. Discriminating between light- and heavy-tailed distributions with limit theorem. PLoS ONE, 10(12):1-23, 2015. [ bib \| DOI ]
	E. Kepten, A. Weron, I. Bronshtein, K. Burnecki, and Y. Garini. Uniform contraction-expansion description of relative centromere and telomere motion. Biophysical Journal, 109(10):1454 - 1462, 2015. [ bib \| DOI ]
	K. Burnecki, E. Kepten, Y. Garini, G. Sikora, and A. Weron. Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors - an alternative approach. Scientific Reports, 5:1-11, 2015. [ bib \| DOI ]
	E. Kepten, A. Weron, G. Sikora, K. Burnecki, and Y. Garini. Guidelines for the fitting of anomalous diffusion mean square displacement graphs from single particle tracking experiments. PLoS ONE, 10(2):1-10, 2015. [ bib \| DOI ]
	K. Burnecki and A. Weron. Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling. Journal of Statistical Mechanics: Theory and Experiment, P10036(10):1-26, 2014. [ bib \| DOI ]
	K. Burnecki and G. Sikora. Estimation of FARIMA parameters in the case of negative memory and stable noise. IEEE Transactions on Signal Processing, 61(11):2825-2835, 2013. [ bib \| DOI ]
	K. Burnecki, E. Kepten, J. B. Janczura, I. Bronshtein, Y. Garini, and A. Weron. Universal algorithm for identification of fractional Brownian motion. a case of telomere subdiffusion. Biophysical Journal, 103(9):1839-1847, 2012. [ bib \| DOI ]
	K. Burnecki, G. Sikora, and A. Weron. Fractional process as a unified model for subdiffusive dynamics in experimental data. Physical Review. E, Statistical Nonlinear and Soft Matter Physics, 86(4):041912-1 - 041912-8, 2012. [ bib \| DOI ]
	K. Burnecki. FARIMA processes with application to biophysical data. Journal of Statistical Mechanics: Theory and Experiment, (5):P05015-1 - P05015-18, 2012. [ bib \| DOI ]
	K. Burnecki, A. Wyłomańska, A. Beletskii, V. Gonchar, and A. Chechkin. Recognition of stable distribution with Lévy index α close to 2. Physical Review. E, Statistical Nonlinear and Soft Matter Physics, 85(5):056711-1 - 056711-8, 2012. [ bib \| DOI ]
	P. Bieńkowski, K. Burnecki, J. B. Janczura, R. Weron, and B. Zubrzak. A new method for automated noise cancellation in electromagnetic field measurement. Journal of Electromagnetic Waves and Applications, 26(8/9):1226-1236, 2012. [ bib \| DOI ]
	K. Burnecki, M. Muszkieta, G. Sikora, and A. Weron. Statistical modelling of subdiffusive dynamics in the cytoplasm of living cells: a FARIMA approach. Europhysics Letters, 98(1):10004-p1 - 10004-p6, 2012. [ bib \| DOI ]
	K. Burnecki, M. Magdziarz, and A. Weron. Identification and validation of fractional subdiffusion dynamics. In J. Klafter, S. C. Lim, and R. Metzler, editors, Fractional dynamics: recent advances, pages 331-351. World Scientific, Singapore [i in.], 2012. [ bib \| DOI ]
	K. Burnecki, J. R. Gajda, and G. Sikora. Stability and lack of memory of the returns of the Hang Seng index. Physica. A, Statistical Mechanics and its Applications, 390(18/19):3136-3146, 2011. [ bib \| DOI ]
	K. Burnecki and M. A. Teuerle. Ruin probability in finite time. In P. Čižek, W. K. Härdle, and R. Weron, editors, Statistical tools for finance and insurance. 2nd Edition, pages 329-348. Springer, Berlin; Heidelberg, 2011. [ bib \| DOI ]
	K. Burnecki, J. B. Janczura, and R. Weron. Building loss models. In P. Čižek, W. K. Härdle, and R. Weron, editors, Statistical tools for finance and insurance. 2nd Edition, pages 293-328. Springer, Berlin; Heidelberg, 2011. [ bib \| DOI ]
	K. Burnecki and A. Weron. Fractional Lévy stable motion can model subdiffusive dynamics. Physical Review. E, Statistical Nonlinear and Soft Matter Physics, 82(2):021130-1 - 021130-8, 2010. [ bib \| DOI ]
	M. Magdziarz, A. Weron, K. Burnecki, and J. Klafter. Fractional Brownian motion versus the continuous-time random walk: A simple test for subdiffusive dynamics. Physical Review Letters, 103(18):180602-1 - 180602-4, 2009. [ bib \| DOI ]
	K. Burnecki, A. Stanislavsky, and K. Weron. Statistical analysis of the maximum energy in solar X-ray flare activity. Acta Physica Polonica B, 40(5):1303-1313, 2009. [ bib \| .pdf ]
	A. Stanislavsky, K. Burnecki, M. Magdziarz, A. Weron, and K. Weron. FARIMA modeling of solar flare activity from empirical time series of soft X-ray solar emission. Astrophysical Journal, 693(2):1877-1882, 2009. [ bib \| DOI ]
	K. Burnecki, J. Klafter, M. Magdziarz, and A. Weron. From solar flare time series to fractional dynamics. Physica. A, Statistical Mechanics and its Applications, 387(5/6):1077-1087, 2008. [ bib \| DOI ]
	K. Burnecki, J. B. Janczura, M. Magdziarz, and A. Weron. Can one see a competition between subdiffusion and Lévy flights? A case of geometric-stable noise. Acta Physica Polonica B, 39(5):1043-1053, 2008. [ bib \| .pdf ]
	K. Burnecki and R. Weron. Visualization tools for insurance risk processes. In Handbook of data visualization, pages 899-920. Springer, Berlin; Heidelberg, 2008. [ bib \| DOI ]
	K. Burnecki and J. Nowicka-Zagrajek. Składka kwantylowa w modelu ryzyka a dane szkodowe z obcięciem dolnym. In Statystyka aktuarialna - stan i perspektywy rozwoju w Polsce. Pod red. W. Ostasiewicza., volume nr 1108 of Prace Naukowe Akademii Ekonomicznej im. Oskara Langego we Wrocławiu, pages 306-317. Wydaw. AE, Wrocław, 2006. [ bib ]
	A. Chernobai, K. Burnecki, S. Rachev, S. Truck, and R. Weron. Modelling cathastrophe claims with left-truncated severity distributions. Computational Statistics, 21:537-555, 2006. [ bib \| DOI ]
	J. Nowicka-Zagrajek and K. Burnecki. Wybrane rodzaje składek w modelu ryzyka kolektywnego. In Inwestycje finansowe i ubezpieczenia - tendencje światowe a polski rynek. Red. nauk. Wanda Ronka-Chmielowiec, Krzysztof Jajuga. T. 2., volume nr 1088 of Prace Naukowe Akademii Ekonomicznej im. Oskara Langego we Wrocławiu, pages 48-55. Wydaw. AE, Wrocław, 2005. [ bib ]
	K. Burnecki, J. Nowicka-Zagrajek, and A. Wyłomańska. Pure risk premiums under deductibles. In Statistical tools for finance and insurance. [Eds] P. Čižek, W. Härdle, R. Weron., pages 427-452. Springer, Berlin, 2005. [ bib \| DOI ]
	K. Burnecki, P. Mista, and A. Weron. Ruin probabilities in finite and infinite time. In Statistical tools for finance and insurance. [Eds] P. Čižek, W. Härdle, R. Weron., pages 341-379. Springer, Berlin, 2005. [ bib \| DOI ]
	K. Burnecki and R. Weron. Modeling of the risk process. In Statistical tools for finance and insurance. [Eds] P. Čižek, W. Härdle, R. Weron., pages 319-339. Springer, Berlin, 2005. [ bib \| DOI ]
	K. Burnecki, A. Misiorek, and R. Weron. Loss distributions. In Statistical tools for finance and insurance. [Eds] P. Čižek, W. Härdle, R. Weron., pages 289-317. Springer, Berlin, 2005. [ bib \| DOI ]
	K. Burnecki, G. Kukla, and D. Taylor. Pricing of catastrophe bonds. In Statistical tools for finance and insurance. [Eds] P. Čižek, W. Härdle, R. Weron., pages 93-114. Springer, Berlin, 2005. [ bib \| DOI ]
	A. Weron, K. Burnecki, S. Mercik, and K. Weron. Complete description of all self-similar models driven by Lévy stable noise. Physical Review. E, Statistical Nonlinear and Soft Matter Physics, 71(1]):016113-1 - 016113-10, 2005. [ bib \| DOI ]
	K. Burnecki, W. Haerdle, and R. Weron. Simulation of risk processes. In J. L Teugels and B. Sundt, editors, Encyclopedia of actuarial science. Vol. 3, pages 1564-1570. Wiley, Chichester, 2004. [ bib ]
	K. Burnecki, P. Miśta, and A. Weron. What is the best approximation of ruin probability in infinite time? Applicationes Mathematicae, 32(2):155-176, 2005. [ bib ]
	K. Burnecki, P. Miśta, and A. Weron. A new gamma type approximation of the ruin probability. Acta Physica Polonica B, 36(5):1473-1483, 2005. [ bib \| .pdf ]
	K. Burnecki, A. Marciniuk, and A. Weron. On annuities under random rates of interest with payments varying in arithmetic and geometric progression. Probability and Mathematical Statistics, 24:1-15, 2004. [ bib \| .pdf ]
	K. Burnecki and A. Weron. Lévy stable processes. From stationary to self-similar dynamics and back. An application to finance. Acta Physica Polonica B, 35(4):1343-1358, 2004. [ bib \| .pdf ]
	K. Burnecki and G. Kukla. Pricing of zero-coupon and coupon cat bonds. Applicationes Mathematicae, 30(3):315-324, 2003. [ bib ]
	K. Burnecki, A. Marciniuk, and A. Weron. Annuities under random rates of interest - revisited. Insurance. Mathematics and Economics, 32(3):457-460, 2003. [ bib \| DOI ]
	S. Mercik, K. Weron, K. Burnecki, and A. Weron. Enigma of self-similarity of fractional Lévy stable motions. Acta Physica Polonica B, 34(7):3773-3791, 2003. [ bib \| .pdf ]
	K. Burnecki and G. Kukla. Obligacje katastroficzne. Krajobraz po wojnie. Asekuracja & Re, (1):29-30, 2003. [ bib ]
	K. Burnecki and Z. Michna. Simulation of Pickands constant. Probability and Mathematical Statistics, 22:193-199, 2002. [ bib \| .pdf ]
	K. Burnecki and G. Kukla. Instrumenty finansowe a ryzyko pogodowe. Asekuracja & Re, (10):26-27, 2001. [ bib ]
	K. Burnecki, J. Nowicka-Zagrajek, and A. Weron. Metoda pomiaru ryzyka (wartości zagrożonej - VaR) na rynku energii elektrycznej. Energetyka, (12):743-747, 2001. [ bib ]
	J. Nowicka-Zagrajek and K. Burnecki. Metody oceny ryzyka ubezpieczeniowego: Cz. 3. Estymacja parametrów rozkładu. Asekuracja & Re, (11):24-25, 2001. [ bib ]
	J. Nowicka-Zagrajek and K. Burnecki. Statystyczne metody oceny ryzyka ubezpieczeniowego: Cz. 2. Asekuracja & Re, (9):24-25, 2001. [ bib ]
	K. Burnecki and J. Nowicka-Zagrajek. Analiza umieralności. Asekuracja & Re, (7):29-30, 2001. [ bib ]
	J. Nowicka-Zagrajek and K. Burnecki. Statystyczne metody oceny ryzyka ubezpieczeniowego: Cz. 1. Asekuracja & Re, (5):20-21, 2001. [ bib ]
	J. Nowicka-Zagrajek and K. Burnecki. Tablice trwania życia. Asekuracja & Re, (4):24-25, 2001. [ bib ]
	K. Burnecki and J. Nowicka-Zagrajek. Czy straty mają ogony... czyli rozkłady żądań stosowane w matematyce ubezpieczeń majątkowych. Asekuracja & Re, (3):22-25, 2001. [ bib ]
	K. Burnecki. Self-similar processes as weak limits of a risk reserve process. Probability and Mathematical Statistics, 20:261-272, 2000. [ bib \| .pdf ]
	K. Burnecki and G. Kukla. Reasekuracja ryzyk ubezpieczeniowych na rynku kapitałowym. Obligacje katastroficzne. Rynek Terminowy, (4):128-134, 2000. [ bib ]
	K. Burnecki, G. Kukla, and R. Weron. Property insurance loss distributions. Physica. A, Statistical Mechanics and its Applications, 287(1/2):269-278, 2000. [ bib \| DOI ]
	K. Burnecki, J. Rosiński, and A. Weron. Spectral representation and structure of stable self-similar processes. In I. Karatzas, B. S. Rajput, and M. S. Taqqu, editors, Stochastic processes and related topics. In Memory of Stamatis Cambanis 1943-1995, Trends in Mathematics, pages 1-14. Birkhauser, Boston [i in.], 1998. [ bib \| DOI \| http ]
	K. Burnecki, M. Maejima, and A. Weron. The Lamperti transformation for self-similar processes. Yokohama Mathematical Journal, 44:25-42, 1997. [ bib ]

Hugo Steinhaus Center Faculty of Pure and Applied Mathematics Wroclaw University of Science and Technology

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Hugo Steinhaus Center
Faculty of Pure and Applied Mathematics
Wroclaw University of Science and Technology