Escaping from an attractor: Importance sampling and rest points I

Abstract

We discuss importance sampling schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. A factor that complicates the analysis is that rest points are included in the domain of interest. We build importance sampling schemes with provably good performance both pre-asymptotically, that is, for fixed size of the noise, and asymptotically, that is, as the size of the noise goes to zero, and that do not degrade as the time horizon gets large. Simulation studies demonstrate the theoretical results.

Published at http://dx.doi.org/10.1214/14-AAP1064 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Dynamic importance sampling for queueing networks
• Importance Sampling for Multiscale Diffusions

Cited by in corpus (5)

• Importance sampling in path space for diffusion processes with slow-fast variables
• A Koopman framework for rare event simulation in stochastic differential equations
• On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting
• Improving control based importance sampling strategies for metastable diffusions via adapted metadynamics
• Symmetrized importance samplers for stochastic differential equations