Stratified Monte Carlo Quadrature for Continuous Random Fields

Konrad Abramowicz () and Oleg Seleznjev ()
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Konrad Abramowicz: Umeå University
Oleg Seleznjev: Umeå University

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 1, 59-72

Abstract: Abstract 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 Hölder 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.

Keywords: Numerical integration; Random field; Sampling design; Stratified sampling; Monte Carlo methods; 60G60; 65D30 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9347-6

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