Yaglom limit for unimodal L\'{e}vy processes

TL;DR

This paper establishes the universal behavior of the Yaglom limit for Lipschitz cones across a broad class of unimodal Lévy processes that are close to the isotropic α-stable Lévy process, highlighting a form of universality in their asymptotic properties.

Contribution

It demonstrates the universality of the Yaglom limit for Lipschitz cones among unimodal Lévy processes near the isotropic α-stable process, extending previous results to a broader class.

Findings

Yaglom limit is universal for Lipschitz cones in unimodal Lévy processes.

Universality holds for processes close to isotropic α-stable Lévy processes.

Results extend understanding of asymptotic behavior in Lévy processes.

Abstract

We prove universality of the Yaglom limit of Lipschitz cones among all unimodal L\'{e}vy processes sufficiently close to the isotropic $\alpha$-stable L\'{e}vy process.