Variational approach to rare event simulation using least-squares regression

Carsten Hartmann; Omar Kebiri; Lara Neureither; Lorenz Richter

doi:10.1063/1.5090271

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arXiv · 1901.09195

Variational approach to rare event simulation using least-squares regression

Carsten Hartmann·Omar Kebiri·Lara Neureither·Lorenz Richter

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Abstract

We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e. zero-variance) change of measure and exploits the fact that the latter can be rephrased as a stochastic optimal control problem. The control problem can be solved by a stochastic approximation algorithm, using the Feynman-Kac representation of the associated dynamic programming equations, and we discuss numerical aspects for high-dimensional problems along with simple toy examples.

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BibTeX RIS

Carsten Hartmann, Omar Kebiri, Lara Neureither, Lorenz Richter. 2019-04-16. Variational approach to rare event simulation using least-squares regression. https://doi.org/10.1063/1.5090271

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