Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime

Ioannis Gasteratos; Michael Salins; Konstantinos Spiliopoulos

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arXiv · 2206.00646

Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime

Ioannis Gasteratos·Michael Salins·Konstantinos Spiliopoulos

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Abstract

We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation scaling allows for a local approximation of the nonlinear dynamics by their linearized version. In addition, we identify a finite-dimensional subspace where exits take place with high probability. Using stochastic control and variational methods we show that our scheme performs well both in the zero noise limit and pre-asymptotically. Simulation studies for stochastically perturbed bistable dynamics illustrate the theoretical results.

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Ioannis Gasteratos, Michael Salins, Konstantinos Spiliopoulos. 2022-06-01. Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime. https://arxiv.org/abs/2206.00646

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