Kebiri, O. and Neureither, L. and Hartmann, C. (2018) Adaptive importance sampling with forwardbackward 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 semilinear dynamic programming equations admit an equivalent formulation as a system of uncoupled forwardbackward 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 highdimensional 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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