Efficient Monte Carlo for high excursions of Gaussian random fields
Robert J. Adler, Jose H. Blanchet, and Jingchen Liu
Source: Ann. Appl. Probab. Volume 22, Number 3
(2012), 1167-1214.
Abstract
Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of excursions above high levels, b. Naïve Monte Carlo takes an exponential, in b, computational cost to estimate these probabilities and conditional expectations for a prescribed relative accuracy. In contrast, our Monte Carlo procedures achieve, at worst, polynomial complexity in b, assuming only that the mean and covariance functions are Hölder continuous. We also explain how to fine tune the construction of our procedures in the presence of additional regularity, such as homogeneity and smoothness, in order to further improve the efficiency.
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Keywords: Gaussian random fields; high-level excursions; Monte Carlo; tail distributions; efficiency
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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1337347542
Digital Object Identifier: doi:10.1214/11-AAP792
Zentralblatt MATH identifier: 06053742
Mathematical Reviews number (MathSciNet): MR2977989
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