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- W2165364936 abstract "Pickands constants play an important role in the exact asymptotic of extreme values for Gaussian stochastic processes. By the generalized Pickands constant Hη we mean the limitHη=limT→∞Hη(T)T,where Hη(T)=Eexp(maxt∈[0,T](2η(t)−ση2(t))) and η(t) is a centered Gaussian process with stationary increments and variance function ση2(t). Under some mild conditions on ση2(t) we prove that Hη 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 ψ(u)=P(supt⩾0ζ(t)−ct>u) as u→∞, where ζ(x)=∫0xZ(s)ds and Z(s) is a stationary centered Gaussian process with covariance function R(t) fulfilling some integrability conditions." @default.
- W2165364936 created "2016-06-24" @default.
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- W2165364936 date "2002-03-01" @default.
- W2165364936 modified "2023-10-18" @default.
- W2165364936 title "Ruin probability for Gaussian integrated processes" @default.
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- W2165364936 doi "https://doi.org/10.1016/s0304-4149(01)00143-0" @default.
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