Ante Mimica

On harmonic functions of symmetric Lévy processes

We consider some classes of Levy processes for which the estimate of Krylov and Safonov (as in [BL02]) fails and thus it is not possible to use the standard iteration technique to obtain a-priori Holder continuity estimates of harmonic functions. Despite the faliure of this method, we obtain some a-priori regularity estimates of harmonic functions for these processes. Moreover, we extend results from [SSV06] and obtain asymptotic behavior of the Green function and the Levy density for a large class of subordinate Brownian motions, where the Laplace exponent of the corresponding subordinator is a slowly varying function.

Estimates of Dirichlet heat kernels for subordinate Brownian motions

In this paper, we discuss estimates of transition densities of subordinate Brownian motions in open subsets of Euclidean space. When

Markov Chain Approximation of Pure Jump Processes

D

Harnack inequalities for subordinate Brownian motions

is a

Intrinsic scaling properties for nonlocal operators

C^{1,1}

Green function estimates for subordinate Brownian motions: Stable and beyond

domain, we establish sharp two-sided estimates for the transition densities of a large class of subordinate Brownian motions in

Heat Kernel Upper Estimates for Symmetric Jump Processes with Small Jumps of High Intensity

D

Analysis of jump processes with nondegenerate jumping kernels

whose scaling order is not necessarily strictly below

Harnack Inequality and Hölder Regularity Estimates for a Lévy Process with Small Jumps of High Intensity

2

Heat kernel estimates for subordinate Brownian motions

. Our estimates are explicit and written in terms of the dimension, the Euclidean distance between two points, the distance to the boundary and Laplace exponent of the corresponding subordinator only.