Recursive computation of the invariant distribution of Markov and Feller processes

TL;DR

This paper introduces a recursive simulation-based method to approximate invariant measures of Markov and Feller processes, applicable to various stochastic models including diffusions with jumps.

Contribution

It extends existing recursive algorithms to a broader class of processes and demonstrates their application in different stochastic regimes.

Findings

Effective approximation of ergodic regimes for Markov and Feller processes.

Applicability to diffusions with jumps and switching regimes.

Validation through multiple stochastic schemes.

Abstract

This paper provides a general and abstract approach to approximate ergodic regimes of Markov and Feller processes. More precisely, we show that the recursive algorithm presented in Lamberton & Pages (2002) and based on simulation algorithms of stochastic schemes with decreasing step can be used to build invariant measures for general Markov and Feller processes. We also propose applications in three different configurations: Approximation of Markov switching Brownian diffusion ergodic regimes using Euler scheme, approximation of Markov Brownian diffusion ergodic regimes with Milstein scheme and approximation of general diffusions with jump components ergodic regimes.