Transition density estimates for jump L\'evy processes

TL;DR

This paper provides explicit upper bounds for the densities of convolution semigroups associated with jump Lévy processes, based on specific assumptions about their Lévy measures and exponents.

Contribution

It introduces new explicit upper density estimates for jump Lévy processes under particular conditions on their Lévy measures and exponents.

Findings

Derived explicit upper bounds for densities of jump Lévy processes.

Established conditions on Lévy measures for density estimates.

Enhanced understanding of the behavior of convolution semigroups in Lévy processes.

Abstract

Upper estimates of densities of convolution semigroups of probability measures are given under explicit assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent.