Malliavin-based multilevel monte carlo estimators for densities of max-stable processes

Abstract

We introduce a class of unbiased Monte Carlo estimators for multivariate densities of max-stable fields generated by Gaussian processes. Our estimators take advantage of recent results on the exact simulation of max-stable fields combined with identities studied in the Malliavin calculus literature and ideas developed in the multilevel Monte Carlo literature. Our approach allows estimating multivariate densities of max-stable fields with precision ε at a computational cost of order O(ε-2log log log (1/ε)).