69 citations · 254 across the 18 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…
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…