Multilevel estimation of expected exit times and other functionals of stopped diffusions
It provides a more efficient method for solving high-dimensional parabolic PDEs via the Feynman-Kac formula, which is important for computational finance and physics.
The paper proposes a multilevel Monte Carlo method for estimating mean exit times of multi-dimensional Brownian diffusions and related functionals, achieving O(ε^{-2} |log ε|^3) complexity for ε root-mean-square error.
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 $\varepsilon$ root-mean-square error is $O(\varepsilon^{-2}\, |\!\log \varepsilon|^3)$.