Fluctuations of empirical means at low temperature for finite Markov chains with rare transitions in the general case |
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Authors: | Isabelle Gaudron Alain Trouvé |
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Affiliation: | (1) CMLA, Ecole Normale Supérieure de Cachan 61, Av. du Président Wilson, F-94235 Cachan Cedex France, FR;(2) Université Paris 13, LAGA, UMR 7539, Avenue Jean-Baptiste Clément, F-93430 Villetaneuse, France, FR |
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Abstract: | Summary. The integrated autocovariance and autocorrelation time are essential tools to understand the dynamical behavior of a Markov chain. We study here these two objects for Markov chains with rare transitions with no reversibility assumption. We give upper bounds for the autocovariance and the integrated autocorrelation time, as well as exponential equivalents at low temperature. We also link their slowest modes with the underline energy landscape under mild assumptions. Our proofs will be based on large deviation estimates coming from the theory of Wentzell and Freidlin and others [4, 3, 12], and on coupling arguments (see [6] for a review on the coupling method). Received 5 August 1996 / In revised form: 6 August 1997 |
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Keywords: | Mathematics Subject Classification (1991): 60F05 60F10 60J10 60M10 65C05 |
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