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

Full text not available from this repository.

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 |
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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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