Estimates of densities for L\'evy processes with lower intensity of large jumps

TL;DR

This paper provides general lower bounds for the transition densities of jump Lévy processes, applicable to various cases including bounded support, exponential decay, and high small jump intensity.

Contribution

It introduces new lower estimate techniques for transition densities of Lévy processes under different Lévy measure conditions.

Findings

Lower bounds for transition densities of Lévy processes.

Applicability to processes with bounded support and exponential decay.

Results for processes with high small jump intensity at small times.

Abstract

We obtain general lower estimates of transition densities of jump L\'evy processes. We use them for processes with L\'evy measures having bounded support, processes with exponentially decaying L\'evy measures for large times and for processes with high intensity of small jumps for small times.