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

Autor:	Gasteratos, Ioannis, Salins, Michael, Spiliopoulos, Konstantinos
Rok vydání:	2022
Předmět:	Mathematics - Probability Mathematics - Optimization and Control Statistics - Methodology 65C05 60G99 60F9
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
Externí odkaz:	http://arxiv.org/abs/2206.00646 Zobrazit plný text záznamu View this record from Arxiv