Extremes of a class of nonhomogeneous Gaussian random fields

• Debicki, Krzysztof ^[1] ; Hashorva, Enkelejd ^[2] ; Ji, Lanpeng ^[2]
  1. [1] University of Wrocław

     University of Wrocław

     Breslavia, Polonia

     
  2. [2] University of Lausanne

     University of Lausanne

     Lausana, Suiza

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 2, 2016, págs. 984-1012
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This contribution establishes exact tail asymptotics of sup(s,t)∈E X(s,t) for a large class of nonhomogeneous Gaussian random fields X on a bounded convex set E⊂R2, 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.