Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime
Autor: | Gasteratos, Ioannis, Salins, Michael, Spiliopoulos, Konstantinos |
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Rok vydání: | 2022 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: Version to appear in Stochastics and Partial Differential Equations: Analysis and Computations. 46 pages |
Databáze: | arXiv |
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