Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Zorawik, Tomasz"'
Autor:
Magdziarz, Marcin, Zorawik, Tomasz
We provide explicit formulas for asymptotic densities of $d$-dimensional isotropic L\'evy walks, when $d>1$. The densities of multidimensional undershooting and overshooting L\'evy walks are presented as well. Interestingly, when the number of dimens
Externí odkaz:
http://arxiv.org/abs/1605.05695
Autor:
Magdziarz, Marcin, Zorawik, Tomasz
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 L\'evy processes. In this comment we show a serious drawback in the derivation of
Externí odkaz:
http://arxiv.org/abs/1512.02020
Autor:
Magdziarz, Marcin, Zorawik, Tomasz
We provide explicit formulas for asymptotic densities of the 2- and 3-dimensional ballistic L\'evy walks. It turns out that in the 3D case the densities are given by elementary functions. The densities of the 2D L\'evy walks are expressed in terms of
Externí odkaz:
http://arxiv.org/abs/1510.05614
Autor:
Magdziarz, Marcin, Zorawik, Tomasz
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-dependent drift and diffusion and time-dependent jump coefficient, the corresp
Externí odkaz:
http://arxiv.org/abs/1509.09051
Autor:
Magdziarz, Marcin, Zorawik, Tomasz
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 fractional differential equations involving fractional material derivative ope
Externí odkaz:
http://arxiv.org/abs/1504.05835
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) killed at 1 and killed or reflected at 0.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/1503.02226
Autor:
Magdziarz, Marcin, Zorawik, Tomasz
Publikováno v:
In Communications in Nonlinear Science and Numerical Simulation 15 June 2019 71:202-211
Autor:
Magdziarz, Marcin, Zorawik, Tomasz
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 February 2018 458(2):1373-1389
Autor:
Magdziarz, Marcin, Zorawik, Tomasz
Publikováno v:
In Communications in Nonlinear Science and Numerical Simulation July 2017 48:462-473
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 July 2016 439(1):91-102