Stratified Monte Carlo Quadrature for Continuous Random Fields
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- 作者：Konrad Abramowicz (1)
Oleg Seleznjev (1)
1. Department of Mathematics and Mathematical Statistics ; Ume氓 University ; 90187 ; Ume氓 ; Sweden - 关键词：Numerical integration ; Random field ; Sampling design ; Stratified sampling ; Monte Carlo methods ; 60G60 ; 65D30
- 刊名：Methodology and Computing in Applied Probability
- 出版年：2015
- 出版时间：March 2015
- 年：2015
- 卷：17
- 期：1
- 页码：59-72
- 全文大小：341 KB
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- 出版者：Springer US
- ISSN：1573-7713
文摘
We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is defined by a finite number of stratified randomly chosen observations with the partition generated by a rectangular grid (or design). We study the class of locally stationary random fields whose local behaviour is like a fractional Brownian field in the mean square sense and find the asymptotic approximation accuracy for a sequence of designs for large number of the observations. For the H枚lder class of random functions, we provide an upper bound for the approximation error. Additionally, for a certain class of isotropic random functions with an isolated singularity at the origin, we construct a sequence of designs eliminating the effect of the singularity point.