Importance sampling for stochastic reaction–diffusion equations in the moderate deviation regime
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Published version
Date
2023-12-08
Authors
Gasteratos, Ioannis
Salins, Michael
Spiliopoulos, Konstantinos
Version
Published version
OA Version
Citation
I. Gasteratos, M. Salins, K. Spiliopoulos. "Importance sampling for stochastic reaction–diffusion equations in the moderate deviation regime" Stochastic Partial Differential Equations. https://doi.org/10.1007/s40072-023-00320-x
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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