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Stratified Monte Carlo quadrature for continuous random fieldsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2015 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 17, no 1, p. 59-72Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

New York: Springer Science+Business Media B.V., 2015. Vol. 17, no 1, p. 59-72
##### Keyword [en]

numerical integration, random field, sampling design, stratified sampling, Monte Carlo methods
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics
##### Identifiers

URN: urn:nbn:se:umu:diva-60994DOI: 10.1007/s11009-013-9347-6ISI: 000349406400005OAI: oai:DiVA.org:umu-60994DiVA, id: diva2:565243
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Available from: 2012-11-06 Created: 2012-11-06 Last updated: 2017-12-07Bibliographically approved
##### In thesis

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.

1. Numerical analysis for random processes and fields and related design problems$(function(){PrimeFaces.cw("OverlayPanel","overlay437283",{id:"formSmash:j_idt705:0:j_idt709",widgetVar:"overlay437283",target:"formSmash:j_idt705:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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