Limit laws on extremes of non-homogeneous Gaussian random fields
Zhongquan Tan
TL;DR
This paper establishes Gumbel limit laws for the maximum of certain non-homogeneous Gaussian random fields, extending to Shepp statistics and storage processes with fractional Brownian motion, using exact tail asymptotics.
Contribution
It proves the Gumbel limit theorem for non-homogeneous Gaussian fields and derives related laws for various Gaussian processes, advancing extreme value theory in this context.
Findings
Gumbel limit law for maxima of non-homogeneous Gaussian fields
Gumbel laws for Shepp statistics of fractional Brownian motion
Gumbel law for storage processes with fractional Brownian motion
Abstract
In this paper, by using the exact tail asymptotics derived by Debicki, Hashorva and Ji (Ann. Probab. 2014), we proved the Gumbel limit theorem for the maximum of a class of non-homogeneous Gaussian random fields. By using the obtained results, we also derived the Gumbel laws for Shepp statistics of fractional Brownian motion and Gaussian integrated process as well as the Gumbel law for Storage process with fractional Brownian motion as input.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Probability and Risk Models · Insurance and Financial Risk Management