Multilevel estimation of expected exit times and other functionals of stopped diffusions

Abstract

This paper proposes and analyzes a new multilevel Monte Carlo method for the estimation of mean exit times for multidimensional Brownian diffusions and associated functionals which correspond to solutions to high-dimensional parabolic PDEs through the Feynman-Kac formula. In particular, it is proved that the complexity to achieve an ε root-mean-square error is O(ε−2 |log ε|3). © 2018 Society for Industrial and Applied Mathematics and American Statistical Association