Large deviations for multiscale diffusion via weak convergence methods
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.
Volume (Year): 122 (2012)
Issue (Month): 4 ()
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Veretennikov, A. Yu., 2000. "On large deviations for SDEs with small diffusion and averaging," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 69-79, September.
- 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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