caa a22 4500 60551951X CHVBK 20210128100730.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s11009-013-9347-6 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9347-6 Stratified Monte Carlo Quadrature for Continuous Random Fields [Elektronische Daten] [Konrad Abramowicz, Oleg Seleznjev] 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. Springer Science+Business Media New York, 2013 Numerical integration nationallicence Random field nationallicence Sampling design nationallicence Stratified sampling nationallicence Monte Carlo methods nationallicence Abramowicz Konrad Department of Mathematics and Mathematical Statistics, Umeå University, 90187, Umeå, Sweden aut Seleznjev Oleg Department of Mathematics and Mathematical Statistics, Umeå University, 90187, Umeå, Sweden aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/1(2015-03-01), 59-72 1387-5841 17:1<59 2015 17 11009 https://doi.org/10.1007/s11009-013-9347-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9347-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Abramowicz Konrad Department of Mathematics and Mathematical Statistics, Umeå University, 90187, Umeå, Sweden aut NATIONALLICENCE 700 1- Seleznjev Oleg Department of Mathematics and Mathematical Statistics, Umeå University, 90187, Umeå, Sweden aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/1(2015-03-01), 59-72 1387-5841 17:1<59 2015 17 11009