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- W2019064047 abstract "Let $$ mathcal{T} $$ be a positive random variable independent of a real-valued stochastic process $$ left{ {X(t),tgeqslant 0} right} $$ . In this paper, we investigate the asymptotic behavior of $$ mathrm{P}left( {{sup_{{tin left[ {0,mathcal{T}} right]}}}X(t)>u} right) $$ as u→∞ assuming that X is a strongly dependent stationary Gaussian process and $$ mathcal{T} $$ has a regularly varying survival function at infinity with index λ ∈ [0, 1). Under asymptotic restrictions on the correlation function of the process, we show that $$ mathrm{P}left( {{sup_{{tin left[ {0,mathcal{T}} right]}}}X(t)>u} right)={c^{lambda }}mathrm{P}left( {mathcal{T}>m(u)} right)left( {1+o(1)} right) $$ with some positive finite constant c and function m(·) defined in terms of the local behavior of the correlation function and the standard Gaussian distribution." @default.
- W2019064047 created "2016-06-24" @default.
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- W2019064047 date "2013-01-01" @default.
- W2019064047 modified "2023-10-03" @default.
- W2019064047 title "Exact tail asymptotics of the supremum of strongly dependent Gaussian processes over a random interval" @default.
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- W2019064047 doi "https://doi.org/10.1007/s10986-013-9196-6" @default.
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