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Stratified Monte Ca...
Stratified Monte Carlo quadrature for continuous random fields
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- Abramowicz, Konrad (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Seleznjev, Oleg (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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(creator_code:org_t)
- 2013-06-06
- 2015
- Engelska.
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Ingår i: Methodology and Computing in Applied Probability. - New York : Springer Science+Business Media B.V.. - 1387-5841 .- 1573-7713. ; 17:1, s. 59-72
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- numerical integration
- random field
- sampling design
- stratified sampling
- Monte Carlo methods
- matematisk statistik
- Mathematical Statistics
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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