69 citations · 254 across the 18 of their papers we have counts for
20 papers
Probability density functions as solutions of heterogeneous Cattaneo-Vernotte diffusion equation
K. Górska, Ž. Tomovski, A. Horzela +1
In this paper, we considered a heterogeneous Cattaneo-Vernotte equation with an exponential type of diffusion coefficient under the fundamental initial and boundary conditions stat…
Stochastic representation of processes with resetting
Marcin Magdziarz, Kacper Taźbierski
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently termi…
A tempered subdiffusive Black-Scholes model
Grzegorz Krzyżanowski, Marcin Magdziarz
In this paper, we focus on the tempered subdiffusive Black-Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option p…
About subordinated generalizations of 3 classical models of option pricing
Michał Balcerek, Grzegorz Krzyżanowski, Marcin Magdziarz
In this paper, we investigate the relation between Bachelier and Black-Scholes models driven by the infinitely divisible inverse subordinators. Such models, in contrast to their cl…
Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate
Foad Shokrollahi, Marcin Marcin Magdziarz
In this paper we propose an extension of the Merton model. We apply the subdiffusive mechanism to analyze equity warrant in a fractional Brownian motion environment, when the short…
First passage time moments of asymmetric Lévy flights
Amin Padash, Aleksei V. Chechkin, Bartłomiej Dybiec +3
We investigate the first-passage dynamics of symmetric and asymmetric Lévy flights in a semi-infinite and bounded intervals. By solving the space-fractional diffusion equation, we…
A computational weighted finite difference method for American and barrier options in subdiffusive Black-Scholes model
Grzegorz Krzyżanowski, Marcin Magdziarz
Subdiffusion is a well established phenomenon in physics. In this paper we apply the subdiffusive dynamics to analyze financial markets. We focus on the financial aspect of time fr…
A weighted finite difference method for subdiffusive Black Scholes Model
Grzegorz Krzyżanowski, Marcin Magdziarz, Łukasz Płociniczak
In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in…
Codifference can detect ergodicity breaking and non-Gaussianity
Jakub Slezak, Ralf Metzler, Marcin Magdziarz
We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of…
Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
Jakub Ślęzak, Ralf Metzler, Marcin Magdziarz
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian…
Method of calculating densities for isotropic Lévy Walks
Marcin Magdziarz, Tomasz Zorawik
We provide explicit formulas for asymptotic densities of -dimensional isotropic Lévy walks, when . The densities of multidimensional undershooting and overshooting Lévy wal…
Comment on "Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Lévy processes" [J. Math. Phys. 53, 072701 (2012)]
Marcin Magdziarz, Tomasz Zorawik
In an article [J. Math. Phys. 53, 072701 (2012)] X. Sun and J. Duan presented Fokker-Planck equations for nonlinear stochastic differential equations with non-Gaussian Lévy process…
Explicit Densities of Multidimensional Lévy Walks
Marcin Magdziarz, Tomasz Zorawik
We provide explicit formulas for asymptotic densities of the 2- and 3-dimensional ballistic Lévy walks. It turns out that in the 3D case the densities are given by elementary funct…
Fractional diffusion equation with distributed-order material derivative. Stochastic foundations
Marcin Magdziarz, Marek Teuerle
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present…
Stochastic representation of fractional subdiffusion equation. The case of infinitely divisible waiting times, Levy noise and space-time-dependent coefficients
Marcin Magdziarz, Tomasz Zorawik
In this paper we analyze fractional Fokker-Planck equation describing subdiffusion in the general infinitely divisible (ID) setting. We show that in the case of space-time-dependen…
Densities of Lévy walks and the corresponding fractional equations
Marcin Magdziarz, Tomasz Zorawik
In this paper we derive explicit formulas for the densities of Levy walks. Our results cover both jump-first and wait-first scenarios. The obtained densities solve certain fraction…
Limit Theorems and Governing Equations for Levy Walks
M. Magdziarz, H. P. Scheffler, P. Straka +1
The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the…
Asymptotic properties of Brownian motion delayed by inverse subordinators
Marcin Magdziarz, Rene L. Schilling
We study the asymptotic behaviour of the time-changed stochastic process , where is a standard one-dimensional Brownian motion an…
Limit theorems for continuous time random walks with continuous paths
Piotr Zebrowski, Marcin Magdziarz
The continuous time random walks (CTRWs) are typically defned in the way that their trajectories are discontinuous step fuctions. This may be a unwellcome feature from the point of…
Statistical Modeling of Solar Flare Activity from Empirical Time Series of Soft X-ray Solar Emission
A. A. Stanislavsky, K. Burnecki, M. Magdziarz +2
A time series of soft X-ray emission observed on 1974-2007 years (GOES) is analyzed. We show that in the periods of high solar activity 1977-1981, 1988-1992, 1999-2003 the energy s…