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).
Classification
subjects
Mathematics
keywords
multilevel; monte carlo; stochastic; numerical analysis; stopped diffusions