Estimates of tempered stable densities

TL;DR

This paper provides estimates for the densities of convolution semigroups of probability measures, focusing on tempered stable semigroups, under specific assumptions related to the Lévy measure and Lévy–Khinchin exponent.

Contribution

It introduces density estimates for convolution semigroups, particularly for tempered stable semigroups, under new assumptions on Lévy measures and exponents.

Findings

Density estimates are derived for tempered stable semigroups.

Results apply under specific assumptions on Lévy measures.

The methods extend previous work on stable and tempered stable processes.

Abstract

Estimates of densities of convolution semigroups of probability measures are given under specific assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent. The assumptions are satisfied, e.g., by tempered stable semigroups of J. Rosi{\'n}ski.