Extremes of a class of non-homogeneous Gaussian random fields

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Serveur académique Lausannois

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info:eu-repo/semantics/altIdentifier/doi/10.1214/14-AOP994

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info:eu-repo/semantics/altIdentifier/urn/urn:nbn:ch:serval-BIB_275851582B2D5

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Serveur Académique Lausannois

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Université de Lausanne et CHUV

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Extremes; nonhomogeneous Gaussian random fields; Shepp statistics; fractional Brownian motion; maximum loss; span of Gaussian processes; Pickands constant; Piterbarg constant; generalized Pickands-Piterbarg constant

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Fields, Random

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K. Debicki et al., « Extremes of a class of non-homogeneous Gaussian random fields », Serveur académique Lausannois, ID : 10.1214/14-AOP994

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This contribution establishes exact tail asymptotics of sup((s,t)) is an element of E X(s,t) for a large class of nonhomogeneous Gaussian random fields X on a bounded convex set E subset of R-2, with variance function that attains its maximum on a segment on E. These findings extend the classical results for homogeneous Gaussian random fields and Gaussian random fields with unique maximum point of the variance. Applications of our result include the derivation of the exact tail asymptotics of the Shepp statistics for stationary Gaussian processes, Brownian bridge and fractional Brownian motion as well as the exact tail asymptotic expansion for the maximum loss and span of stationary Gaussian processes.

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