Stratified Monte Carlo Quadrature for Continuous Random Fields |
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Authors: | Email author" target="_blank">Konrad?AbramowiczEmail author Oleg?Seleznjev |
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Institution: | 1.Department of Mathematics and Mathematical Statistics,Ume? University,Ume?,Sweden |
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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. |
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