On Shift Harnack Inequalities for Subordinate Semigroups and Moment Estimates for L\'evy Processes

TL;DR

This paper demonstrates that shift Harnack inequalities are maintained under Bochner's subordination and provides new moment estimates for subordinators and general Lévy processes, advancing understanding in stochastic analysis.

Contribution

It establishes the preservation of shift Harnack inequalities under subordination and introduces novel moment estimates for subordinators and Lévy processes.

Findings

Shift Harnack inequalities are preserved under Bochner's subordination.

New moment estimates for subordinators are derived.

Moment estimates for general Lévy processes are established.

Abstract

We show that shift Harnack type inequalities (in the sense of F.-Y.~Wang \cite{Wan14}) are preserved under Bochner's subordination. The proofs are based on two types of moment estimates for subordinators. As a by-product we establish moment estimates for general L\'evy processes.