Fluctuations of Interacting Markov Chain Monte Carlo Methods

TL;DR

This paper establishes a multivariate central limit theorem for a broad class of interacting MCMC algorithms, providing theoretical insights into their fluctuation behavior around limiting measures.

Contribution

It introduces a novel theoretical framework using resolvent operators and semigroup techniques to analyze fluctuations in nonlinear interacting MCMC algorithms.

Findings

Proves a multivariate central limit theorem for these algorithms.

Provides a new analytical approach for fluctuation analysis.

Enhances understanding of the stochastic behavior of interacting MCMC methods.

Abstract

We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the class of nonlinear Markov chains interacting with their empirical occupation measures. We develop an original theoretical analysis based on resolvent operators and semigroup techniques to analyze the fluctuations of their occupation measures around their limiting values.