UBC - University of British Columbia (Vancouver Campus, , 2329 West Mall, Vancouver, BC Canada V6T 1Z4 -
Okanagan Campus, 3333 University Way, Kelowna, BC Canada V1V 1V7 - Canada)
5Statistics - Department of Statistics (DEPARTMENT OF STATISTICS 333-6356 Agricultural Road University of British Columbia Vancouver, BC, V6T 1Z2 Tel: 604 822 0570 Fax: 604 822 6960 - Canada)
UBC - University of British Columbia (Vancouver Campus, , 2329 West Mall, Vancouver, BC Canada V6T 1Z4 -
Okanagan Campus, 3333 University Way, Kelowna, BC Canada V1V 1V7 - Canada)
Abstract : We present a functional central limit theorem for a general class of interacting Markov chain Monte Carlo interpretations of discrete generation measure-valued equations. The path space models associated with these stochastic processes 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 fluctuation of their occupation measures around their limiting value. We also present a set of simple regularity conditions that applies to interacting Markov chain Monte Carlo models on path spaces, yielding what seems to be the first fluctuation theorems for this class of self-interacting models.
https://hal.inria.fr/inria-00227536
Contributor : Pierre Del Moral
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Submitted on : Tuesday, February 5, 2008 - 11:29:33 AM
Last modification on : Friday, April 19, 2019 - 3:24:18 PM
Document(s) archivé(s) le : Friday, November 25, 2016 - 8:36:51 PM
Bernard Bercu, Pierre Del Moral, Arnaud Doucet. Fluctuations of Interacting Markov Chain Monte Carlo Models. Stochastic Processes and their Applications, Elsevier, 2012, 122 (4), pp.1304-1331. ⟨inria-00227536v5⟩
