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

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 ).