Bottom crossing probability for symmetric jump processes (full version)

TL;DR

This paper analyzes the decay rate of the bottom crossing probability for symmetric jump processes, providing results applicable to stable-like and subordinated diffusion processes on fractals and similar spaces.

Contribution

It determines the decay rate of bottom crossing probabilities for symmetric jump processes under heat kernel estimates, extending to fractal-like spaces.

Findings

Decay rate characterized under heat kernel conditions

Applicable to stable-like processes on fractals

Results extend to stable-subordinated diffusions

Abstract

We determine the decay rate of the bottom crossing probability for symmetric jump processes under the condition on heat kernel estimates. Our results are applicable to symmetric stable-like processes and stable-subordinated diffusion processes on a class of (unbounded) fractals and fractal-like spaces.