Bottom crossing probability for symmetric jump processes (full version)

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.

Appendix B.3 is corrected. The short version (which does not include appendices) is accepted for publication in Mathematische Zeitschrift