86 citations · 347 across the 33 of their papers we have counts for
27 papers · 1 filter
Asymptotics of transition densities for Lévy processes with stochastic resetting
Kacper Budnik, Tomasz Grzywny, Paweł Sztonyk
We derive an explicit representation for the distribution of a Lévy process with total stochastic resetting and use it to investigate the asymptotic behaviour of the corresponding…
Stationary states for stable processes with partial resetting
Tomasz Grzywny, Karol Szczypkowski, Zbigniew Palmowski +1
We study a -dimensional stochastic process which arises from a Lévy process by partial resetting, that is the position of the process at a…
Asymptotic expansion of the nonlocal heat content
Tomasz Grzywny, Julia Lenczewska
Let be a Lévy process in and be an open subset of with finite Lebesgue measure. In this article we consider the qua…
Subordinated Markov processes: sharp estimates for heat kernels and Green functions
Tomasz Grzywny, Bartosz Trojan
We prove sharp estimates on heat kernels and Green functions for subordinate Markov processes with both discrete an continuous time, under relatively weak assumptions about origina…
Yaglom limit for unimodal Lévy processes
Gavin Armstrong, Krzysztof Bogdan, Tomasz Grzywny +2
We prove universality of the Yaglom limit of Lipschitz cones among all unimodal Lévy processes sufficiently close to the isotropic -stable Lévy process.
Hitting probabilities for Lévy processes on the real line
Tomasz Grzywny, Łukasz Leżaj, Maciej Miśta
We prove sharp two-sided estimates on the tail probability of the first hitting time of bounded interval as well as its asymptotic behaviour for general non-symmetric processes whi…
First exit times from a bounded interval for Lévy processes
Tomasz Grzywny
In this paper we study the mean of the first exit time from a bounded interval of various Lévy processes. We establish sharp two-sided estimates of the mean for Lévy processes unde…
L{é}vy processes: concentration function and heat kernel bounds
Tomasz Grzywny, Karol Szczypkowski
We investigate densities of vaguely continuous convolution semigroups of probability measures on . We expose that many typical conditions on the characteristic expone…
Transition densities of subordinators of positive order
Tomasz Grzywny, Łukasz Leżaj, Bartosz Trojan
We prove existence and asymptotic behavior of the transition density for a large class of subordinators whose Laplace exponents satisfy lower scaling condition at infinity. Further…
Estimates of heat kernels of non-symmetric Lévy processes
Tomasz Grzywny, Karol Szczypkowski
We investigate densities of vaguely continuous convolution semigroups of probability measures on . First, we provide results that give upper estimates in a situation…
Spectral Heat Content for Lévy Processes
Tomasz Grzywny, Hyunchul Park, Renming Song
In this paper we study the spectral heat content for various Lévy processes. We establish the asymptotic behavior of the spectral heat content for Lévy processes of bounded variati…
A note on the generalized heat content for Lévy processes
Wojciech Cygan, Tomasz Grzywny
Let be a Lévy process in and be an open subset of with finite Lebesgue measure. The quantity $H (t) = \int_Ω \mathb…
Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes
Tomasz Grzywny, Mateusz Kwaśnicki
In the first part of this article, we prove two-sided estimates of hitting probabilities of balls, the potential kernel and the Green function for a ball for general isotropic unim…
Asymptotic behaviour and estimates of slowly varying convolution semigroups
Tomasz Grzywny, Michał Ryznar, Bartosz Trojan
We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on under the assumption that its…
Heat content for convolution semigroups
Wojciech Cygan, Tomasz Grzywny
Let be a Lévy process in and be an open subset of with finite Lebesgue measure. In this article we consider the qua…
Estimates of Dirichlet heat kernel for symmetric Markov processes
Tomasz Grzywny, Kyung-Youn Kim, Panki Kim
We consider a large class of symmetric pure jump Markov processes dominated by isotropic unimodal Lévy processes with weak scaling conditions. First, we establish sharp two-sided h…
Asymptotic behavior of densities of unimodal convolution semigroups
Wojciech Cygan, Tomasz Grzywny, Bartosz Trojan
We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on under the assumption that its L…
Hitting times of points and intervals for symmetric Lévy processes
Tomasz Grzywny, Michał Ryznar
For one-dimensional symmetric Lévy processes, which hit every point with positive probability, we give sharp bounds for the tail function of the first hitting time of B which is ei…
Dirichlet heat kernel for unimodal Lévy processes
K. Bogdan, T. Grzywny, M. Ryznar
We estimate the heat kernel of the smooth open set for the isotropic unimodal pure-jump Lévy process with infinite Lévy measure and weakly scaling Lévy-Kchintchine exponent.
Barriers, exit time and survival probability for unimodal Lévy processes
Krzysztof Bogdan, Tomasz Grzywny, Michał Ryznar
We construct superharmonic functions and give sharp bounds for the expected exit time and probability of survival for isotropic unimodal Lévy processes
On Harnack inequality and Hölder regularity for isotropic unimodal Lévy processes
Tomasz Grzywny
We prove the scale invariant Harnack inequality and regularity properties for harmonic functions with respect to an isotropic unimodal Lévy process with the characteristic exponent…
Potential theory of one-dimensional geometric stable processes
Tomasz Grzywny, Michał Ryznar
The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $α…
Heat kernel estimates for the fractional Laplacian with Dirichlet conditions
Krzysztof Bogdan, Tomasz Grzywny, Michał Ryznar
We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.
Heat kernel of fractional Laplacian in cones
Krzysztof Bogdan, Tomasz Grzywny
We give sharp estimates for the transition density of the isotropic stable Lévy process killed when leaving a right circular cone.