Asymptotics of supremum distribution of a Gaussian process over a Weibullian time
نویسندگان
چکیده
Let {X(t) : t ∈ [0,∞)} be a centered Gaussian process with stationary increments and variance function σ X(t). We study the exact asymptotics of P(supt∈[0,T ] X(t) > u), as u → ∞, where T is an independent of {X(t)} nonnegative Weibullian random variable. As an illustration we work out the asymptotics of supremum distribution of fractional Laplace motion.
منابع مشابه
Logarithmic Asymptotics for the Supremum of a Stochastic Process1 by Ken Duffy,2
Logarithmic asymptotics are proved for the tail of the supremum of a stochastic process, under the assumption that the process satisfies a restricted large deviation principle on regularly varying scales. The formula for the rate of decay of the tail of the supremum, in terms of the underlying rate function, agrees with that stated by Duffield and O’Connell [Math. Proc. Cambridge Philos. Soc. (...
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