Support theorem for L\'evy driven SDEs

TL;DR

This paper establishes a support theorem for the probability law of solutions to stochastic differential equations driven by jump processes, offering insights into the behavior of such systems with degenerate jump noises.

Contribution

It introduces a support theorem applicable to general jump-driven SDEs, expanding understanding of their solution distributions.

Findings

Support theorem for jump SDEs established

Applicable to degenerate jump noise cases

Provides detailed support descriptions for solutions

Abstract

We provide a support theorem for the law of the solution to an SDE with jump noise. This theorem applies to general SDEs with jumps and is illustrated by examples of SDEs with quite degenerate jump noises where the theorem leads to an informative description of the support.