Ruin probability for Gaussian integrated processes

Krzysztof Debicki

Stochastic Processes and their Applications, 2002, vol. 98, issue 1, 151-174

Abstract: Pickands constants play an important role in the exact asymptotic of extreme values for Gaussian stochastic processes. By the generalized Pickands constant we mean the limitwhere and [eta](t) is a centered Gaussian process with stationary increments and variance function [sigma][eta]2(t). Under some mild conditions on [sigma][eta]2(t) we prove that is well defined and we give a comparison criterion for the generalized Pickands constants. Moreover we prove a theorem that extends result of Pickands for certain stationary Gaussian processes. As an application we obtain the exact asymptotic behavior of as u-->[infinity], where and Z(s) is a stationary centered Gaussian process with covariance function R(t) fulfilling some integrability conditions.

Keywords: Exact; asymptotics; Extremes; Fractional; Brownian; motion; Gaussian; process; Logarithmic; asymptotics; Pickands; constants (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (7)

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