2014/05/31 by Krzysztof Dȩbicki, Krzysztof Dȩbicki, Enkelejd Hashorva +1 · 26 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Bounded function #Brownian bridge #Brownian motion #Financial Risk and Volatility Modeling #Fractional Brownian motion #Gaussian #Gaussian process #Gaussian random field #Probability and Risk Models #Random field #Random function #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.1214/14-aop994
published in The Annals of Probability 44(2) (Institute of Mathematical Statistics) · Published at http://dx.doi.org/10.1214/14-AOP994 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2016/03/01 · arxiv created 2016/03/15 · arxiv updated 2016/03/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
This contribution establishes exact tail asymptotics of sup(s,t)\inE 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.