On asymptotic constants in the theory of extremes for Gaussian processes

A. B. Dieker · Benjamin Yakir

66 citations0/0 files storedBernoulli

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Probability and Risk Models Probability and Statistical Research Statistical Distribution Estimation and Applications

Abstract

This paper gives a new representation of Pickands’ constants, which arise in the study of extremes for a variety of Gaussian processes. Using this representation, we resolve the long-standing problem of devising a reliable algorithm for estimating these constants. A detailed error analysis illustrates the strength of our approach.

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References

1987Tests for Hurst Effect 1995Discretization Error in Simulation of One-Dimensional Reflecting Brownian Motion 2002Ruin probability for Gaussian integrated processes

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2017Generalized Pickands constants and stationary max-stable processes 2015Extremes of vector-valued Gaussian processes: Exact asymptotics 2015Bounds for expected maxima of Gaussian processes and their discrete approximations 2014Piterbarg theorems for chi-processes with trend

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