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October 2015 Escaping from an attractor: Importance sampling and rest points I
Paul Dupuis, Konstantinos Spiliopoulos, Xiang Zhou
Ann. Appl. Probab. 25(5): 2909-2958 (October 2015). DOI: 10.1214/14-AAP1064

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.

Citation

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Paul Dupuis. Konstantinos Spiliopoulos. Xiang Zhou. "Escaping from an attractor: Importance sampling and rest points I." Ann. Appl. Probab. 25 (5) 2909 - 2958, October 2015. https://doi.org/10.1214/14-AAP1064

Information

Received: 1 March 2013; Revised: 1 June 2014; Published: October 2015
First available in Project Euclid: 30 July 2015

zbMATH: 1334.65007
MathSciNet: MR3375891
Digital Object Identifier: 10.1214/14-AAP1064

Subjects:
Primary: 60G99, 65C05
Secondary: 60F99

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 5 • October 2015
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