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May 2012 Tail approximations of integrals of Gaussian random fields
Jingchen Liu
Ann. Probab. 40(3): 1069-1104 (May 2012). DOI: 10.1214/10-AOP639

Abstract

This paper develops asymptotic approximations of P(Tef(t)dt > b) as b → ∞ for a homogeneous smooth Gaussian random field, f, living on a compact d-dimensional Jordan measurable set T. The integral of an exponent of a Gaussian random field is an important random variable for many generic models in spatial point processes, portfolio risk analysis, asset pricing and so forth.

The analysis technique consists of two steps: 1. evaluate the tail probability P(Ξef(t)dt > b) over a small domain Ξ depending on b, where mes(Ξ)0 as b → ∞ and mes() is the Lebesgue measure; 2. with Ξ appropriately chosen, we show that P(Tef(t)dt > b) = (1 + o(1)) mes(T) mes1(Ξ) P(Ξef(t)dt > b).

Citation

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Jingchen Liu. "Tail approximations of integrals of Gaussian random fields." Ann. Probab. 40 (3) 1069 - 1104, May 2012. https://doi.org/10.1214/10-AOP639

Information

Published: May 2012
First available in Project Euclid: 4 May 2012

zbMATH: 1266.60092
MathSciNet: MR2962087
Digital Object Identifier: 10.1214/10-AOP639

Subjects:
Primary: 60F10 , 60G70

Keywords: Extremes , Gaussian random field

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 3 • May 2012
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