Path Results for Symmetric Jump Processes

TL;DR

This paper studies a class of symmetric jump processes in Euclidean space, establishing lower bounds on occupation times and proving a support theorem, advancing understanding of their path properties.

Contribution

It introduces new bounds on occupation times and proves a support theorem for symmetric jump processes associated with non-local Dirichlet forms.

Findings

Lower bounds on occupation times of sets

Support theorem for symmetric jump processes

Enhanced understanding of path properties

Abstract

We consider a class of jump processes in euclidean space which are associated to a certain non-local symmetric Dirichlet form. We prove a lower bound on the occupation times of sets, and that a support theorem holds for these processes.