On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting

Charles-Edouard Bréhier; Tony Lelièvre

doi:10.1063/1.5081440

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arXiv · 1811.06289

On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting

Charles-Edouard Bréhier·Tony Lelièvre

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Abstract

We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We introduce a new, very general and effective family of score functions which is designed for these problems. We illustrate its behavior on a series of numerical experiments. In particular, we demonstrate how it can be used to estimate large deviation rate functionals for the longtime limit of temporal averages.

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Charles-Edouard Bréhier, Tony Lelièvre. 2018-11-15. On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting. https://doi.org/10.1063/1.5081440

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