Averaging for some simple constrained Markov processes

TL;DR

This paper investigates a class of constrained Markov processes with fast dynamics, applying a penalty method to derive an averaging result as the underlying dynamic accelerates infinitely, and fully characterizes the resulting averaged process.

Contribution

It introduces a novel averaging approach for constrained Markov processes with fast dynamics using a penalty method, providing a detailed description of the averaged process.

Findings

Averaging result obtained via penalty method for infinitely accelerated dynamics

Full characterization of the averaged piecewise deterministic Markov process

Applicable to a class of constrained Markov processes with fast underlying dynamics

Abstract

In this paper, a class of piecewise deterministic Markov processes with underlying fast dynamic is studied. Using a "penalty method" , an averaging result is obtained when the underlying dynamic is infinitely accelerated. The features of the averaged process, which is still a piecewise deterministic Markov process, are fully described.