16 citations · 35 across the 5 of their papers we have counts for
6 papers
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…
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…
Fourier-Bessel heat kernel estimates
Jacek Malecki, Grzegorz Serafin, Tomasz Zorawik
We provide sharp two-sided estimates of the Fourier-Bessel heat kernel and we give sharp two-sided estimates of the transition probability density for the Bessel process in (0,1) k…