On Time Reversal of Piecewise Deterministic Markov Processes

TL;DR

This paper investigates the time reversal of stationary piecewise deterministic Markov processes (PDMPs), deriving the parameters of the reversed process such as jump intensity and measure, enhancing understanding of their temporal symmetries.

Contribution

It provides a general framework for characterizing the time-reversed process of stationary PDMPs, including explicit formulas for key parameters.

Findings

Derived formulas for jump intensity in reversed PDMPs

Characterized the jump measure of the reversed process

Extended understanding of temporal symmetry in PDMPs

Abstract

We study the time reversal of a general PDMP. The time reversed process is defined as $X_{(T-t)-}$, where $T$ is some given time and $X_t$ is a stationary PDMP. We obtain the parameters of the reversed process, like the jump intensity and the jump measure.