Tractability of Monte Carlo integration in Hermite spaces

TL;DR

This paper investigates the computational feasibility of Monte Carlo integration in Hermite spaces, providing criteria for when such integration is tractable in high dimensions.

Contribution

It establishes necessary and sufficient conditions for the tractability of Monte Carlo integration in Hermite spaces defined by Hermite coefficient decay.

Findings

Provides criteria for tractability in high-dimensional integration

Characterizes function spaces via Hermite coefficient decay

Identifies conditions for efficient Monte Carlo integration

Abstract

We consider multivariate integration in the randomized setting. The function spaces which we study are defined on R^s with respect to the Gaussian measure and the functions are characterized by the decay of their Hermite coefficients. We study tractability of Monte Carlo integration and give necessary and sufficient conditions to achieve tractability.