Stratified Monte Carlo Quadrature for Continuous Random Fields
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 60551951X | ||
| 003 | CHVBK | ||
| 005 | 20210128100730.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150301xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s11009-013-9347-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s11009-013-9347-6 | ||
| 245 | 0 | 0 | |a Stratified Monte Carlo Quadrature for Continuous Random Fields |h [Elektronische Daten] |c [Konrad Abramowicz, Oleg Seleznjev] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media New York, 2013 | ||
| 690 | 7 | |a Numerical integration |2 nationallicence | |
| 690 | 7 | |a Random field |2 nationallicence | |
| 690 | 7 | |a Sampling design |2 nationallicence | |
| 690 | 7 | |a Stratified sampling |2 nationallicence | |
| 690 | 7 | |a Monte Carlo methods |2 nationallicence | |
| 700 | 1 | |a Abramowicz |D Konrad |u Department of Mathematics and Mathematical Statistics, Umeå University, 90187, Umeå, Sweden |4 aut | |
| 700 | 1 | |a Seleznjev |D Oleg |u Department of Mathematics and Mathematical Statistics, Umeå University, 90187, Umeå, Sweden |4 aut | |
| 773 | 0 | |t Methodology and Computing in Applied Probability |d Springer US; http://www.springer-ny.com |g 17/1(2015-03-01), 59-72 |x 1387-5841 |q 17:1<59 |1 2015 |2 17 |o 11009 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s11009-013-9347-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s11009-013-9347-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Abramowicz |D Konrad |u Department of Mathematics and Mathematical Statistics, Umeå University, 90187, Umeå, Sweden |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Seleznjev |D Oleg |u Department of Mathematics and Mathematical Statistics, Umeå University, 90187, Umeå, Sweden |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Methodology and Computing in Applied Probability |d Springer US; http://www.springer-ny.com |g 17/1(2015-03-01), 59-72 |x 1387-5841 |q 17:1<59 |1 2015 |2 17 |o 11009 | ||