Web page of my grant SONATA BIS
PUBLICATIONS – MARCIN MAGDZIARZ:
Preprints of my publications can be downloaded
HERE
1)
Magdziarz M., "A note on distributions with complete
monotone derivative", in preparation (2021).
2)
Shokrollahi F., Magdziarz M.,
"Equity warrant pricing under subdiffusive
fractional Brownian motion of the short rate", submitted (2020).
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3)
Krzyżanowski
G., Magdziarz M., "A tempered subdiffusive Black-Scholes model", Fract.
Calc. Appl. Anal., Mathematica Applicanda, accepted
(2024).
4)
Balcerek M., Krzyżanowski
G., Magdziarz M., " About subordinated
generalizations of 3 classical models of option pricing", accepted (2024).
5)
Janczura J., Magdziarz M., Metzler, R., „Parameter estimation of the
fractional Ornstein-Uhlenbeck process based on
quadratic variation”, Chaos 33 2023, 103125 (2023).
6)
Magdziarz M., Zebrowski P., "Functional convergence of
continuous-time random walks with continuous paths", Communications in
Contemporary Mathematics 25, 2150106
(2023).
7)
Magdziarz M., Taźbierski K.,"
Stochastic representation of processes with resetting", Phys. Rev. E 106,
014147 (2022).
8)
Magdziarz M., Szczotka W.,
"Levy walks with rests: long-time analysis", Phys. Rev. E 105, 014114
(2022).
9)
Błażejczyk P., Magdziarz M.,
"Stochastic modeling of Levy-like human eye movements", Chaos 31,
043129 (2021).
10) Krzyżanowski G., Magdziarz M.,
"A computational weighted finite difference method for American and
Barrier options in subdiffusive Black Scholes
Model", Comm. Nonlinear Sci. Num. Sim. 96, 105676 (2021).
11) Carnaffan S., Magdziarz M., Szczotka W., "Nonlinear dynamics of continuous-time
random walks in inhomogeneous medium", Chaos 30, 063135 (2020).
12) Krzyżanowski G., Magdziarz M., Płociniczak Ł., "A weighted finite difference method
for subdiffusive Black Scholes model", Computers
& Mathematics with Applications 80, 653–670 (2020).
13) Padash A., Chechkin A.V., Dybiec B., Magdziarz M., Shokri
B., Metzler R., "First passage time moments of asymmetric Levy
flights", J. Phys. A: Math. Theor. 53, 275002 (2020).
14) Satora M., Magdziarz M., Rząsa A., Rypuła K., Płoneczka-Janeczko K., "Insight into the intestinal
microbiome of farrowing sows following the administration of garlic (Allium
sativum) extract and probiotic bacteria cultures under farming
conditions", BMC Vet. Research (2020).
15) Magdziarz M., Zorawik T.,
"Limit properties of Levy walks", J. Phys. A: Math. Theor. (2020).
16) Magdziarz M., "Lamperti
transformation of scaled Brownian motion and related Langevin equations",
Comm. Nonlinear Sci. Num. Sim. 83, 105077 (2020).
17) Slezak J.K., Metzler R., Magdziarz,
M., "Codifference can detect ergodicity breaking
and non-Gaussianity", New J. Phys 21, 053008
(2019).
18) Mackala A., Magdziarz M.,
"Statistical analysis of superstatistical
fractional Brownian motion and applications", Phys. Rev. E 99, 012143
(2019).
19) Magdziarz M., Zorawik T.,
"Lamperti transformation - cure for ergodicity
breaking", Comm. Nonlinear Sci. Num. Sim. 71, 202–211 (2019).
20) Magdziarz M., Szczotka W.,
"Diffusion limit of Levy-Lorentz gas is Brownian motion", Comm.
Nonlinear Sci. Num. Sim. 60,
100–106 (2018).
21) Magdziarz M., Szczotka W.,
"Coupled continuous time-random walks in quenched random
environment", J. Stat. Mech. 023207 (2018).
22) Slezak J.K., Metzler R., Magdziarz,
M., "Superstatistical generalised
Langevin equation", New J. Phys 20, 023026 (2018).
23) Magdziarz M., Zorawik T.,
"Ergodic properties of Levy flights coexisting with subdiffusion
and related models", J. Math. Anal. Appl. 458, 1373–1389 (2018).
24) Magdziarz M., Teuerle M.,
"Fractional diffusion equation with distributed-order material derivative.
Stochastic foundations", J. Phys. A: Math. Theor.
50, 184005 (2017).
25) Magdziarz M., Zorawik T.,
" Method of calculating densities for isotropic ballistic Lévy walks
", Comm. Nonlinear Sci. Num. Sim. 48, 462–473 (2017)
26) Karipova G., Magdziarz M.,
" Pricing of basket options in subdiffusive
fractional Black-Scholes model", Chaos, Solitons and Fractals 102, 245–253
(2017).
27) Magdziarz M., Zorawik T.,
"Aging ballistic Levy walks", Phys. Rev. E., 95, 022126 (2017).
28) Magdziarz M., Zorawik T.,
"Densities of scaling limits of coupled continuous time random
walks", Fract. Calc. Appl. Anal. 19, 1488–1506
(2016).
29) Shokrollahi F., Kilicman A., Magdziarz M., " Pricing European options and currency
options by time changed mixed fractional Brownian motion with transaction
costs", Int. J. Financial Eng. 3, 1650003 (2016).
30) Magdziarz M., Zorawik T.,
"Explicit densities of multidimensional ballistic Levy walks", Phys. Rev. E., 94, 022130 (2016).
31) Magdziarz M., Zorawik T.,
" Comment on "Fokker-Planck equations for nonlinear dynamical systems
driven by non-Gaussian Lévy processes'' [J. Math. Phys. 53, 072701 (2012)]
", J. Math. Phys. 57, 034101
(2016).
32) Magdziarz M., Zorawik T.,
"Stochastic representation of fractional subdiffusion
equation. The case of infinitely divisible waiting times, Levy noise and
space-time-dependent coefficients", Proc. Amer. Math. Soc. 144, 1767-1778 (2016).
33) Magdziarz M., Szczotka W.,
"Quenched trap model for Levy flights", Comm. Nonlinear Sci. Num.
Sim. 30, 5–14 (2016).
34) Magdziarz M, Scheffler H-P., Straka
P., Zebrowski P., "Limit theorems and governing equations for Levy
walks", Stoch. Proc. Appl., 125, 4021–4038 (2015).
35) Annunziato M., Borzi A., Magdziarz
M., Weron. A, " A fractional
Fokker-Planck control framework for subdiffusion
processes ", Optim. Control Appl. Meth. 37,
290–304 (2016).
36) Magdziarz M., Schilling R.L., "Asymptotic
properties of Brownian motion delayed by inverse subordinators", Proc.
Amer. Math. Soc., 143, 4485–4501 (2015).
37) Magdziarz M., Teuerle M.,
"Asymptotic properties and numerical simulation of multidimensional Levy
walks", Comm. Nonlinear Sci. Num. Sim. 20, 489-505 (2015).
38) Slezak J.K., Magdziarz,
M., "Rotational invariance of
stochastic process with application to fractional dynamics", J. Stat. Mech.
P10028 (2014).
39) Gajda J., Magdziarz M., "Large deviations for subordinated
Brownian motion and applications", Statist. Probab.
Lett., 88, 149-156 (2014).
40) Magdziarz M., Gajda J., Zorawik T., "Comment on fractional Fokker-Planck
equation with space and time dependent drift and diffusion", J. Stat.
Phys., 154, 1241-1250 (2014).
41) Magdziarz M., Szczotka W.,
Zebrowski P., "Asymptotic behavior of random walks with correlated
temporal structure", Proc. Royal Soc. A, 469, 20130419 (2013).
42) Magdziarz, M., Wojcik J., Slezak J.K., "Estimation and testing of Hurst
parameter using p-variation", J. Phys. A: Math. Theor.,
46, 325003 (2013)
43) Teuerle M., Zebrowski P., Magdziarz
M., "Multidimensional Levy walk and its scaling limits", J. Phys. A:
Math. Theor., 45, 385002 (2012).
44) Magdziarz M., Teuerle M.,
Zebrowski P., "Scaling limits of overshooting Levy walks", Acta Phys.
Polon. B, 43, 1111 (2012).
45) Magdziarz M., Gajda J.
"Anomalous dynamics of Black-Scholes model time-changed by inverse
subordinators", Acta Phys. Polon. B, 43, 1093
(2012).
46) Magdziarz M., Metzler R., Szczotka
W., Zebrowski P., "Correlated continuous time random walks in external
force fields", Phys. Rev. E., 85, 051103 (2012).
47) Magdziarz M., Metzler R., Szczotka
W., Zebrowski P., "Correlated continuous time random walks – scaling
limits and Langevin picture", J. Stat. Mech., P04010 (2012).
48) Magdziarz M., Szczotka W.,
Zebrowski P., "Langevin picture of Levy walks and their extensions",
J. Stat. Phys., 147, 74-96 (2012).
49) Magdziarz M., Weron A.,
"Anomalous diffusion: Testing ergodicity breaking in experimental
data", Phys. Rev. E 84, 051138 (2011).
50) Gajda J., Magdziarz M., "Kramers’
escape problem for fractional Klein-Kramers equation
with tempered ?-stable waiting times", Phys. Rev. E, 84, 021137 (2011).
51) Magdziarz M., Orzeł S., Weron A., "Option pricing in subdiffusive
Bachelier model", J. Stat. Phys., 145, 187-203
(2011).
52) Magdziarz M., Weron A.,
"Ergodic properties of anomalous diffusion processes", Ann. Phys.,
326, 2431-2443. (2011).
53) Burnecki K., Magdziarz M., Weron A., "Identification and validation of fractional
subdiffusion dynamics", Chapter in the book
"Fractional Dynamics" J. Klafter, S.C. Lim,
R. Metzler (Eds.) (World Scientific, Singapore, 2011).
54) Weron A., Magdziarz M.
"Generalization of the Khinchin theorem to Levy
flights", Phys. Rev. Lett., 105, 260603 (2010).
55) Gajda J., Magdziarz M.
"Fractional Fokker-Planck equation with tempered alpha-stable waiting
times. Langevin picture and computer simulation", Phys. Rev. E, 82,
011117 (2010).
56) Magdziarz M., Klafter J.
"Detecting origins of subdiffusion. P-variation
test for confined systems.", Phys. Rev. E, 82, 011129 (2010).
57) Weron K., Jurlewicz A., Magdziarz M., Weron A., Trzmiel J. "Over- and undershoot subordination
scenario for fractional two-power-law relaxation responses", Phys. Rev. E,
81, 041123 (2010).
58) Magdziarz M. "Path properties of subdiffusion – a martingale approach", Stochastic
Models, 26, 256-271 (2010).
59) Magdziarz M. "A note on Maruyama's mixing
theorem", Theory Probab. Appl., 54, 407-409 (2009).
60) Magdziarz M., Weron A., Burnecki K., Klafter J.
"Fractional Brownian motion vs continuous-time random walk: A simple test
for subdiffusive dynamics", Phys. Rev. Lett.,
103, 180602 (2009).
61) Weron A., Magdziarz M.
"Anomalous diffusion and semimartingales",
EPL, 86, 60010 (2009).
62) Magdziarz M. "Black-Scholes formula in subdiffusive regime", J. Stat. Phys., 136, 553-564
(2009).
63) Magdziarz M. "Correlation cascades, ergodic
properties and long memory of infinitely divisible processes", Stoch.
Proc. Appl., 119, 3416-3434 (2009).
64) Magdziarz M. "Stochastic representation of subdiffusion processes with time-dependent drift",
Stoch. Proc. Appl., 119, 3238-3252 (2009).
65) Magdziarz M. "Langevin picture of subdiffusion with infinitely divisible waiting times",
J. Stat. Phys., 135, 763-772 (2009).
66) Stanislavsky A.A., Burnecki
K., Magdziarz M, Weron A., Weron K., "FARIMA Modelling of Solar Flare Activity
from Empirical Time Series of Soft X-ray Solar Emission", Astrophys. J., 693, 1877-1882 (2009) .
67) Magdziarz M., Weron A., Klafter J. "Equivalence of the fractional
Fokker-Planck and subordinated Langevin equations: The case of time-dependent
force", Phys. Rev. Lett., 101, 210601 (2008).
68) Burnecki K., Janczura J., Magdziarz M., Weron A. "Can
one see a competition between subdiffusion and Levy
flights? A case of geometric-stable noise", Acta Phys. Polon.
B 39 (5), 1043-1054 (2008).
69) Weron A., Magdziarz
M., Weron K.
"Modeling of subdiffusion in
space-time-dependent force fields beyond the fractional Fokker-Planck
equation", Phys. Rev. E, 77, 036704 (2008).
70) Burnecki K., Klafter J., Magdziarz M., Weron A. "
From solar flare time series to fractional dynamics", Physica
A, 387, 1077-1087 (2008).
71) Magdziarz M. "Fractional Ornstein-Uhlenbeck processes. Joseph effect in models with infinite
variance", Physica A, 387, 123-133 (2008).
72) Magdziarz M., Weron A.
"Numerical approach to the fractional Klein-Kramers
equation", Phys. Rev. E, 76, 066708 (2007).
73) Klafter J., Koren T., Magdziarz M. "First passage times of Levy Flights
coexisting with subdiffusion", Phys. Rev. E ,
76, 031129 (2007).
74) Magdziarz M. "Short and long memory fractional
Ornstein-Uhlenbeck alpha-stable processes",
Stochastic Models, 23:3, 451 - 473 (2007).
75) Magdziarz M.,
Weron A. "Fractional Langevin equation
with alpha-stable noise.A link to fractional ARIMA
time series", Studia Mathematica, 181(1), 47-60 (2007).
76) Magdziarz M., Weron
A. "Competition between subdiffusion and Levy
flights: A Monte Carlo approach", Phys. Rev. E, 75, 056702 (2007).
77) Magdziarz M., Mista
P, Weron A. "Anomalous diffusion approximation
of risk processes in collective risk theory", Acta Phys. Polon. B, 38, 1647-1656 (2007).
78) Magdziarz M., Weron
A., Weron K. "Fractional Fokker-Planck dynamics:
Stochastic representation and computer simulation", Phys. Rev. E, 75,
016708 (2007).
79) Magdziarz M., Weron
K. "Anomalous diffusion schemes underlying the Cole-Cole relaxation. The
role of the inverse-time." Physica A 367, 1-6
(2006).
80) Magdziarz M., Weron
K. "Anomalous diffusion schemes underlying the stretched exponential
relaxation. The role of subordinators" Acta Phys. Polon.B
37 (5): 1617-1625 (2006).
81) Weron K., Jurlewicz A.,
Magdziarz M. "Havriliak-Negami Response in the
Framework of the Continuous-Time Random Walk", Acta Phys. Polon. B 36 (5): 1855-1868, (2005).
82) Magdziarz M. "The dependence structure of
the fractional Ornstein-Uhlenbeck process", Probab. Math. Statist. 25(1), 97-104 (2005).