Stratified Monte Carlo quadrature for continuous random fields
2015 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 17, no 1, 59-72 p.Article in journal (Refereed) Published
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 behavior 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¨older 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.
Place, publisher, year, edition, pages
New York: Springer Science+Business Media B.V., 2015. Vol. 17, no 1, 59-72 p.
numerical integration, random field, sampling design, stratified sampling, Monte Carlo methods
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:umu:diva-60994DOI: 10.1007/s11009-013-9347-6ISI: 000349406400005OAI: oai:DiVA.org:umu-60994DiVA: diva2:565243