4.2 Article

EFFICIENT CONDITIONAL MONTE CARLO SIMULATIONS FOR THE EXPONENTIAL INTEGRALS OF GAUSSIAN RANDOM FIELDS

Journal

JOURNAL OF APPLIED PROBABILITY
Volume 59, Issue 2, Pages 366-383

Publisher

CAMBRIDGE UNIV PRESS
DOI: 10.1017/jpr.2021.57

Keywords

Exponential integral; Asmussen-Kroese estimator; logarithmically efficient estimators; rare event simulation

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This paper investigates the problem of probability estimation for a continuous Gaussian random field on a compact set. It proposes a conditional Monte Carlo type estimator and discusses its asymptotic properties.
We consider a continuous Gaussian random field living on a compact set T subset of R-d. We are interested in designing an asymptotically efficient estimator of the probability that the integral of the exponential of the Gaussian process over T exceeds a large threshold u. We propose an Asmussen-Kroese conditional Monte Carlo type estimator and discuss its asymptotic properties according to the assumptions on the first and second moments of the Gaussian random field. We also provide a simulation study to illustrate its effectiveness and compare its performance with the importance sampling type estimator of Liu and Xu (2014a).

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