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Submitted to the Annals of Applied Probability EFFICIENT MONTE CARLO FOR HIGH EXCURSIONS OF
 

Summary: Submitted to the Annals of Applied Probability
EFFICIENT MONTE CARLO FOR HIGH EXCURSIONS OF
GAUSSIAN RANDOM FIELDS
By Robert J. Adler
Jose H. Blanchet
and Jingchen Liu
Technion, Columbia, Columbia
Our focus is on the design and analysis of efficient Monte Carlo meth-
ods 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. NaĻive 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, as-
suming only that the mean and covariance functions are HĻolder 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.
1. Introduction. This paper centers on the design and analysis of efficient
Monte Carlo techniques for computing probabilities and conditional expectations

  

Source: Adler, Robert J. - Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology

 

Collections: Mathematics; Engineering