Tractability of Monte Carlo integration in Hermite spaces
arXiv:1502.01166h-index: 7
Originality Synthesis-oriented
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For researchers in numerical integration, it clarifies when Monte Carlo methods are efficient in high-dimensional Hermite spaces.
The paper studies multivariate integration in Hermite spaces under Gaussian measure, providing necessary and sufficient conditions for tractability of Monte Carlo integration.
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.