# Malliavin-based Multilevel Monte Carlo Estimators for Densities of Max-stable Processes

## TL;DR

This paper presents a novel unbiased Monte Carlo estimator for the multivariate density of max-stable fields, leveraging Malliavin calculus and multilevel Monte Carlo techniques to achieve efficient and precise density estimation.

## Contribution

It introduces a new class of unbiased estimators for max-stable field densities that combine recent simulation methods with Malliavin calculus and multilevel Monte Carlo ideas.

## Key findings

- Achieves density estimation with error ε at cost O(ε^{-2} log log log(1/ε)).
- Utilizes recent exact simulation techniques for max-stable fields.
- Integrates Malliavin calculus with multilevel Monte Carlo for improved efficiency.

## Abstract

We introduce a class of unbiased Monte Carlo estimators for the multivariate density of max-stable fields generated by Gaussian processes. Our estimators take advantage of recent results on 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 $\varepsilon $ at a computational cost of order $O\left( \varepsilon ^{-2}\log \log \log \left( 1/\varepsilon \right) \right) $.