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Large deviations for multiscale diffusion via weak convergence methods

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  • Dupuis, Paul
  • Spiliopoulos, Konstantinos
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    Abstract

    We study the large deviations principle for locally periodic SDEs with small noise and fast oscillating coefficients. There are three regimes depending on how fast the intensity of the noise goes to zero relative to homogenization parameter. We use weak convergence methods which provide convenient representations for the action functional for all regimes. Along the way, we study weak limits of controlled SDEs with fast oscillating coefficients. We derive, in some cases, a control that nearly achieves the large deviations lower bound at prelimit level. This control is useful for designing efficient importance sampling schemes for multiscale small noise diffusion.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 4 ()
    Pages: 1947-1987

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1947-1987

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    Related research

    Keywords: Large deviations; Multiscale diffusion; Importance sampling; Rugged energy landscape;

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    1. Freidlin, Mark I. & Sowers, Richard B., 1999. "A comparison of homogenization and large deviations, with applications to wavefront propagation," Stochastic Processes and their Applications, Elsevier, vol. 82(1), pages 23-52, July.
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