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Two Mathematical Tools to Analyze Metastable Stochastic Processes

In: Numerical Mathematics and Advanced Applications 2011

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  • T. Leliévre

    (Université Paris-Est, CERMICS, Ecole des Ponts Paristech
    INRIA Rocquencourt, MicMac project team)

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.

Suggested Citation

  • T. Leliévre, 2013. "Two Mathematical Tools to Analyze Metastable Stochastic Processes," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 791-810, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_83
    DOI: 10.1007/978-3-642-33134-3_83
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