Repository: Freie Universit├Ąt Berlin, Math Department

Adaptive importance sampling with forward-backward stochastic differential equations

Kebiri, Omar and Neureither, Lara and Hartmann, Carsten (2019) Adaptive importance sampling with forward-backward stochastic differential equations. In: Stochastic Dynamics Out of Equilibrium. Springer Proceedings in Mathematics & Statistics, 282 . Springer International Publishing, pp. 265-281. ISBN 978-3-030-15095-2

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Official URL: https://doi.org/10.1007/978-3-030-15096-9_7

Abstract

We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating functions, which appear relevant in the context of, e.g.~molecular dynamics, and we discuss the construction of an optimal (i.e. minimum variance) change of measure by solving a stochastic control problem. We show that the associated semi-linear dynamic programming equations admit an equivalent formulation as a system of uncoupled forward-backward stochastic differential equations that can be solved efficiently by a least squares Monte Carlo algorithm. We illustrate the approach with a suitable numerical example and discuss the extension of the algorithm to high-dimensional systems.

Item Type:Book Section
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2221
Deposited By: Silvia Hoemke
Deposited On:16 Feb 2018 15:35
Last Modified:11 Feb 2022 13:58

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