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Moderate deviations-based importance sampling for stochastic recursive equations

Part of: Limit theorems Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  17 November 2017

Paul Dupuis  and
Dane Johnson
Paul Dupuis*
Affiliation:
Brown University
Dane Johnson*
Affiliation:
University of North Carolina at Chapel Hill
*
* Postal address: Division of Applied Mathematics, Brown University, Box F, 182 George St., Providence, RI 02912, USA.
** Postal address: Department of Statistics and Operations Research, University of Carolina at Chapel Hill, 318 Hanes Hall, Chapel Hill, NC 27599, USA. Email address: [email protected]
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Abstract

Subsolutions to the Hamilton–Jacobi–Bellman equation associated with a moderate deviations approximation are used to design importance sampling changes of measure for stochastic recursive equations. Analogous to what has been done for large deviations subsolution-based importance sampling, these schemes are shown to be asymptotically optimal under the moderate deviations scaling. We present various implementations and numerical results to contrast their performance, and also discuss the circumstances under which a moderate deviation scaling might be appropriate.

Keywords

Moderate deviationsimportance samplingrare eventaccelerated Monte Carlo

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60F10: Large deviations
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 4 , December 2017 , pp. 981 - 1010
Copyright
Copyright © Applied Probability Trust 2017 

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