Large deviations for multiscale diffusion via weak convergence methods

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Dupuis, Paul¹  Spiliopoulos, Konstantinos¹ 

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

关键词: Large deviations;    Multiscale diffusion;    Importance sampling;    Rugged energy landscape;   

DOI  :  10.1016/j.spa.2011.12.006

来源: Elsevier

【 摘 要 】

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. (c) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free