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Fluctuations of interacting Markov chain Monte Carlo methods

Authors
Journal
Stochastic Processes and their Applications
0304-4149
Publisher
Elsevier
Volume
122
Issue
4
Identifiers
DOI: 10.1016/j.spa.2012.01.001
Keywords
  • Multivariate Central Limit Theorems
  • Random Fields
  • Martingale Limit Theorems
  • Self-Interacting Markov Chains
  • Markov Chain Monte Carlo Algorithms
Disciplines
  • Computer Science
  • Mathematics

Abstract

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.

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