Repository: Freie Universität Berlin, Math Department

Adaptive importance sampling with forward-backward stochastic differential equations

Kebiri, O. and Neureither, L. and Hartmann, C. (2018) Adaptive importance sampling with forward-backward stochastic differential equations. Proceedings of the Institut Henri Poincaré . (Submitted)

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Official URL: http://arxiv.org/abs/1802.04981

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:Article
Additional Information:SFB 1114 Preprint in SciRate.arXiv:1802.04981
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:16 Feb 2018 15:52

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