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

Abstract

This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional 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 $\epsilon$ root-mean-square error is $O({\epsilon }^{-2}|\log \epsilon {|}^3)$.

arXiv comment21 pages, 3 figures, to appear in SIAM/ASA Journal on Uncertainty Quantification