Supports of Invariant Measures for Piecewise Deterministic Markov Processes

TL;DR

This paper characterizes the supports of invariant measures for certain piecewise deterministic Markov processes by analyzing the controllability of an associated deterministic control system, linking invariant control sets to the supports.

Contribution

It introduces a novel approach connecting invariant measure supports to invariant control sets via controllability analysis of associated control systems.

Findings

Supports are characterized by invariant control sets.

Controllability properties determine the structure of invariant measures.

Provides a framework for analyzing invariant measures in PDMPs.

Abstract

For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant control sets determine the supports.