Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime
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.
Cite
@article{arxiv.2206.00646,
title = {Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime},
author = {Ioannis Gasteratos and Michael Salins and Konstantinos Spiliopoulos},
journal= {arXiv preprint arXiv:2206.00646},
year = {2023}
}
Comments
Version to appear in Stochastics and Partial Differential Equations: Analysis and Computations. 46 pages