Large Deviations for Multiscale Diffusions via Weak Convergence Methods

Details Large Deviations for Multiscale Diffusions via Weak Convergence Methods Large Deviations for Multiscale Diffusions via Weak Convergence Methods

2010-11-26

arxiv.org/abs/1011.5933v1

Stochastic Processes and their Applications 122 (2012), pp. 1947-1987

Mathematics

Probability

Scientific paper

10.1016/j.spa.2011.12.006

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

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