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On the Density Functions of Integrals of Gaussian Random Fields

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  22 February 2016

Jingchen Liu  and
Gongjun Xu
Jingchen Liu*
Affiliation:
Columbia University
Gongjun Xu*
Affiliation:
Columbia University
*
∗ Postal address: Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, NY 10027, USA.
∗ Postal address: Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, NY 10027, USA.
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Abstract

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In the paper we consider the density functions of random variables that can be written as integrals of exponential functions of Gaussian random fields. In particular, we provide closed-form asymptotic bounds for the density functions and, under smoothness conditions, we derive exact tail approximations of the density functions.

Keywords

Gaussian random fieldintegraldensity function

MSC classification

Primary: 60F10: Large deviations 60G70: Extreme value theory; extremal processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 2 , June 2013 , pp. 398 - 424
Copyright
© Applied Probability Trust 

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