The Annals of Applied Probability

Escaping from an attractor: Importance sampling and rest points I

Paul Dupuis, Konstantinos Spiliopoulos, and Xiang Zhou

Full-text: Open access

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.

Article information

Source
Ann. Appl. Probab., Volume 25, Number 5 (2015), 2909-2958.

Dates
Received: March 2013
Revised: June 2014
First available in Project Euclid: 30 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1438261056

Digital Object Identifier
doi:10.1214/14-AAP1064

Mathematical Reviews number (MathSciNet)
MR3375891

Zentralblatt MATH identifier
1334.65007

Subjects
Primary: 65C05: Monte Carlo methods 60G99: None of the above, but in this section
Secondary: 60F99: None of the above, but in this section

Keywords
Importance sampling Monte Carlo methods large deviations equilibrium points attractors

Citation

Dupuis, Paul; Spiliopoulos, Konstantinos; Zhou, Xiang. Escaping from an attractor: Importance sampling and rest points I. Ann. Appl. Probab. 25 (2015), no. 5, 2909--2958. doi:10.1214/14-AAP1064. https://projecteuclid.org/euclid.aoap/1438261056


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References

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