On a new class of score functions to estimate tail probabilities of some stochastic processes with adaptive multilevel splitting - Bréhier, Charles-Edouard; Lelièvre, Tony (Chaos (Woodbury, N.Y.), 2019)
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.