On the Conditional Distributions and the Efficient Simulations of Exponential Integrals of Gaussian Random FieldsReport as inadecuate



 On the Conditional Distributions and the Efficient Simulations of Exponential Integrals of Gaussian Random Fields


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In this paper, we consider the extreme behavior of a Gaussian random field $ft$ living on a compact set $T$. In particular, we are interested in tail events associated with the integral $\int {T} e^{ft}dt$. We construct a non-Gaussian random field whose distribution can be explicitly stated. This field approximates the conditional Gaussian random field $f$ given that $\int {T} e^{ft}dt$ exceeds a large value in total variation. Based on this approximation, we show that the tail event of $\int {T} e^{ft}dt$ is asymptotically equivalent to the tail event of $\sup T \gamma t$ where $\gammat$ is a Gaussian process and it is an affine function of $ft$ and its derivative field. In addition to the asymptotic description of the conditional field, we construct an efficient Monte Carlo estimator that runs in polynomial time of $\log b$ to compute the probability $P\int {T} e^{ft}dt b$ with a prescribed relative accuracy.



Author: Jingchen Liu; Gongjun Xu

Source: https://archive.org/



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