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On a new class of score functions to estimate tail probabilities of some stochastic processes with adaptive
Charles-Edouard Bréhier1, Tony Lelièvre2
1Univ Lyon, CNRS, Université Claude Bernard Lyon 1, UMR5208, Institut Camille Jordan, F-69622 Villeurbanne, France.
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 that is designed for these problems. We illustrate its behavior in a series of numerical experiments. In particular, we demonstrate how it can be used to estimate large deviations rate functionals for the longtime limit of temporal averages.
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