Two Mathematical Tools to Analyze Metastable Stochastic Processes

T. Leliévre ()
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T. Leliévre: Université Paris-Est, CERMICS, Ecole des Ponts Paristech

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 791-810 from Springer

Abstract: Abstract We present how entropy estimates and logarithmic Sobolev inequalities on the one hand, and the notion of quasi-stationary distribution on the other hand, are useful tools to analyze metastable overdamped Langevin dynamics, in particular to quantify the degree of metastability. We discuss the interest of these approaches to estimate the efficiency of some classical algorithms used to speed up the sampling, and to evaluate the error introduced by some coarse-graining procedures. This paper is a summary of a plenary talk given by the author at the ENUMATH 2011 conference.

Keywords: Markov Chain Monte Carlo Method; Exit Point; Logarithmic Sobolev Inequality; Continuous State Space; Canonical Measure (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-642-33134-3_83

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