On a new class of score functions to estimate tail probabilities of some stochastic processes with adaptive multilevel splitting

Chaos. 2019 Mar;29(3):033126. doi: 10.1063/1.5081440.

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.