Vol. 13, No. 2, 2018

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Symmetrized importance samplers for stochastic differential equations

Andrew Leach, Kevin K. Lin and Matthias Morzfeld

Vol. 13 (2018), No. 2, 215–241
Abstract

We study a class of importance sampling methods for stochastic differential equations (SDEs). A small noise analysis is performed, and the results suggest that a simple symmetrization procedure can significantly improve the performance of our importance sampling schemes when the noise is not too large. We demonstrate that this is indeed the case for a number of linear and nonlinear examples. Potential applications, e.g., data assimilation, are discussed.

Keywords
importance sampling, stochastic differential equations, small noise theory, symmetrization, data assimilation
Mathematical Subject Classification 2010
Primary: 65C05
Milestones
Received: 7 July 2017
Revised: 7 March 2018
Accepted: 25 March 2018
Published: 5 June 2018
Authors
Andrew Leach
Program in Applied Mathematics
University of Arizona
Tucson, AZ
United States
Google
Mountain View, CA
United States
Kevin K. Lin
Program in Applied Mathematics
University of Arizona
Tucson, AZ
United States
Department of Mathematics
University of Arizona
Tucson, AZ
United States
Matthias Morzfeld
Program in Applied Mathematics
University of Arizona
Tucson, AZ
United States
Department of Mathematics
University of Arizona
Tucson, AZ
United States