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)
Magdziarz M., Taźbierski K.," Stochastic representation of
processes with resetting", submitted (2021).
3)
Magdziarz M., Szczotka W., "Levy walks
with rests – long-time analysis", submitted (2021).
4)
Balcerek M., Krzyżanowski G.,
Magdziarz M., " About subordinated generalizations of 3 classical models
of option pricing", submitted (2021).
5)
Krzyżanowski G., Magdziarz M., "A tempered subdiffusive Black-Scholes model", submitted (2021).
6)
Shokrollahi F., Magdziarz M., "Equity
warrant pricing under subdiffusive fractional
Brownian motion of the short rate", submitted (2020).
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7)
Magdziarz M., Zebrowski P., "Functional convergence of
continuous-time random walks with continuous paths", accepted to
Communications in Contemporary Mathematics (2021).
8)
Błażejczyk P., Magdziarz M., "Stochastic
modeling of Levy-like human eye movements", Chaos 31, 043129 (2021).
9)
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).
10) Carnaffan S., Magdziarz M., Szczotka W., "Nonlinear dynamics of continuous-time
random walks in inhomogeneous medium", Chaos 30, 063135 (2020).
11) Krzyżanowski G., Magdziarz M., Płociniczak Ł., "A weighted finite difference method
for subdiffusive Black Scholes model", Computers
& Mathematics with Applications 80, 653–670 (2020).
12) 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).
13) 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).
14) Magdziarz M., Zorawik
T., "Limit properties of Levy walks", J. Phys. A: Math. Theor. (2020).
15) Magdziarz M., "Lamperti transformation of scaled Brownian motion and
related Langevin equations", Comm. Nonlinear Sci. Num. Sim. 83, 105077
(2020).
16) Slezak J.K., Metzler R., Magdziarz,
M., "Codifference can detect ergodicity breaking
and non-Gaussianity", New J. Phys 21, 053008
(2019).
17) Mackala A., Magdziarz M., "Statistical
analysis of superstatistical fractional Brownian
motion and applications", Phys. Rev. E 99, 012143 (2019).
18) Magdziarz M., Zorawik
T., "Lamperti transformation - cure for
ergodicity breaking", Comm. Nonlinear Sci. Num. Sim. 71, 202–211 (2019).
19) Magdziarz M., Szczotka
W., "Diffusion limit of Levy-Lorentz gas is Brownian motion", Comm.
Nonlinear Sci. Num. Sim. 60,
100–106 (2018).
20) Magdziarz M., Szczotka
W., "Coupled continuous time-random walks in quenched random
environment", J. Stat. Mech. 023207 (2018).
21) Slezak J.K., Metzler R., Magdziarz,
M., "Superstatistical generalised
Langevin equation", New J. Phys 20, 023026 (2018).
22) Magdziarz M., Zorawik
T., "Ergodic properties of Levy flights coexisting with subdiffusion and related models", J. Math. Anal. Appl.
458, 1373–1389 (2018).
23) Magdziarz M., Teuerle
M., "Fractional diffusion equation with distributed-order material
derivative. Stochastic foundations", J. Phys. A: Math. Theor.
50, 184005 (2017).
24) Magdziarz M., Zorawik
T., " Method of calculating densities for isotropic ballistic Lévy walks
", Comm. Nonlinear Sci. Num. Sim. 48, 462–473 (2017)
25) Karipova G., Magdziarz M., " Pricing of
basket options in subdiffusive fractional
Black-Scholes model", Chaos, Solitons and Fractals 102, 245–253 (2017).
26) Magdziarz M., Zorawik
T., "Aging ballistic Levy walks", Phys. Rev. E., 95, 022126 (2017).
27) Magdziarz M., Zorawik
T., "Densities of scaling limits of coupled continuous time random
walks", Fract. Calc. Appl. Anal. 19, 1488–1506
(2016).
28) 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).
29) Magdziarz M., Zorawik
T., "Explicit densities of multidimensional ballistic Levy
walks", Phys. Rev. E., 94,
022130 (2016).
30) 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).
31) 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).
32) Magdziarz M., Szczotka
W., "Quenched trap model for Levy flights", Comm. Nonlinear Sci. Num.
Sim. 30, 5–14 (2016).
33) Magdziarz M, Scheffler H-P., Straka P., Zebrowski P., "Limit theorems and governing
equations for Levy walks", Stoch. Proc. Appl., 125, 4021–4038 (2015).
34) 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).
35) Magdziarz M., Schilling R.L.,
"Asymptotic properties of Brownian motion delayed by inverse
subordinators", Proc. Amer. Math. Soc., 143, 4485–4501 (2015).
36) Magdziarz M., Teuerle
M., "Asymptotic properties and numerical simulation of multidimensional
Levy walks", Comm. Nonlinear Sci. Num. Sim. 20, 489-505 (2015).
37) Slezak J.K., Magdziarz, M., "Rotational invariance of stochastic
process with application to fractional dynamics", J. Stat. Mech.
P10028 (2014).
38) Gajda J.,
Magdziarz M., "Large deviations for subordinated Brownian motion
and applications", Statist. Probab. Lett., 88,
149-156 (2014).
39) 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).
40) Magdziarz M., Szczotka
W., Zebrowski P., "Asymptotic behavior of random walks with correlated
temporal structure", Proc. Royal Soc. A, 469, 20130419 (2013).
41) Magdziarz, M., Wojcik J., Slezak
J.K., "Estimation and testing of
Hurst parameter using p-variation", J. Phys. A: Math. Theor.,
46, 325003 (2013)
42) Teuerle M., Zebrowski P., Magdziarz M.,
"Multidimensional Levy walk and its scaling limits", J. Phys. A:
Math. Theor., 45, 385002 (2012).
43) Magdziarz M., Teuerle
M., Zebrowski P., "Scaling limits of overshooting Levy walks", Acta
Phys. Polon. B, 43, 1111 (2012).
44) Magdziarz M., Gajda
J. "Anomalous dynamics of Black-Scholes model time-changed by inverse
subordinators", Acta Phys. Polon. B, 43, 1093
(2012).
45) Magdziarz M., Metzler R., Szczotka W., Zebrowski P., "Correlated continuous time
random walks in external force fields", Phys. Rev. E., 85, 051103 (2012).
46) Magdziarz M., Metzler R., Szczotka W., Zebrowski P., "Correlated continuous time
random walks – scaling limits and Langevin picture", J. Stat. Mech.,
P04010 (2012).
47) Magdziarz M., Szczotka
W., Zebrowski P., "Langevin picture of Levy walks and their
extensions", J. Stat. Phys., 147,
74-96 (2012).
48) Magdziarz M., Weron
A., "Anomalous diffusion: Testing ergodicity breaking in experimental
data", Phys. Rev. E 84, 051138 (2011).
49) Gajda J.,
Magdziarz M., "Kramers’ escape problem
for fractional Klein-Kramers equation with tempered
α-stable waiting times", Phys. Rev. E, 84, 021137 (2011).
50) Magdziarz M., Orzeł
S., Weron A., "Option pricing in subdiffusive Bachelier
model", J. Stat. Phys., 145, 187-203 (2011).
51) Magdziarz M., Weron
A., "Ergodic properties of anomalous diffusion processes", Ann.
Phys., 326, 2431-2443. (2011).
52) 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).
53) Weron A., Magdziarz M.
"Generalization of the Khinchin theorem to Levy
flights", Phys. Rev. Lett., 105, 260603 (2010).
54) 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).
55) Magdziarz M., Klafter
J. "Detecting origins of subdiffusion.
P-variation test for confined systems.", Phys. Rev. E, 82, 011129 (2010).
56) 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).
57) Magdziarz M. "Path properties
of subdiffusion – a martingale approach",
Stochastic Models, 26, 256-271 (2010).
58) Magdziarz M. "A note on
Maruyama's mixing theorem", Theory Probab.
Appl., 54, 407-409 (2009).
59) 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).
60) Weron A., Magdziarz M. "Anomalous
diffusion and semimartingales", EPL, 86, 60010
(2009).
61) Magdziarz M. "Black-Scholes
formula in subdiffusive regime", J. Stat. Phys.,
136, 553-564 (2009).
62) Magdziarz M. "Correlation
cascades, ergodic properties and long memory of infinitely divisible
processes", Stoch. Proc. Appl., 119, 3416-3434 (2009).
63) Magdziarz M. "Stochastic
representation of subdiffusion processes with
time-dependent drift", Stoch. Proc. Appl., 119, 3238-3252 (2009).
64) Magdziarz M. "Langevin picture
of subdiffusion with infinitely divisible waiting
times", J. Stat. Phys., 135, 763-772
(2009).
65) 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) .
66) 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).
67) 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).
68) 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).
69) Burnecki K., Klafter
J., Magdziarz M., Weron A. " From solar flare
time series to fractional dynamics", Physica A,
387, 1077-1087 (2008).
70) Magdziarz M. "Fractional
Ornstein-Uhlenbeck processes. Joseph effect in models
with infinite variance", Physica A, 387, 123-133
(2008).
71) Magdziarz M., Weron
A. "Numerical approach to the fractional Klein-Kramers
equation", Phys. Rev. E, 76, 066708 (2007).
72) Klafter J., Koren
T., Magdziarz M. "First passage times of Levy Flights coexisting with subdiffusion", Phys. Rev. E , 76, 031129 (2007).
73) Magdziarz M. "Short and long
memory fractional Ornstein-Uhlenbeck alpha-stable
processes", Stochastic Models, 23:3, 451 - 473 (2007).
74) 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).
75) Magdziarz M., Weron
A. "Competition between subdiffusion and Levy
flights: A Monte Carlo approach", Phys. Rev. E, 75, 056702 (2007).
76) Magdziarz M., Mista
P, Weron A. "Anomalous diffusion approximation
of risk processes in collective risk theory", Acta Phys. Polon. B, 38, 1647-1656 (2007).
77) Magdziarz M., Weron
A., Weron K. "Fractional Fokker-Planck dynamics:
Stochastic representation and computer simulation", Phys. Rev. E, 75,
016708 (2007).
78) Magdziarz M., Weron
K. "Anomalous diffusion schemes underlying the Cole-Cole relaxation. The
role of the inverse-time." Physica A 367, 1-6
(2006).
79) 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).
80) 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).
81) Magdziarz M. "The dependence
structure of the fractional Ornstein-Uhlenbeck
process", Probab. Math. Statist. 25(1), 97-104
(2005).