# 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.

Autor: Jingchen Liu; Gongjun Xu

Fuente: https://archive.org/