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arXiv · 1802.04981

Adaptive importance sampling with forward-backward stochastic differential equations

Omar Kebiri·Lara Neureither·Carsten Hartmann
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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.

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Omar Kebiri, Lara Neureither, Carsten Hartmann. 2019-01-29. Adaptive importance sampling with forward-backward stochastic differential equations. https://arxiv.org/abs/1802.04981

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