Asymptotics of supremum distribution of a Gaussian process over a Weibullian time
Arendarczyk, Marek ; Dȩbicki, Krzysztof
Bernoulli, Tome 17 (2011) no. 1, p. 194-210 / Harvested from Project Euclid
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Let {X(t) : t∈[0, ∞)} be a centered Gaussian process with stationary increments and variance function σX2(t). We study the exact asymptotics of ℙ(sup t∈[0, T]X(t)>u) as u→∞, where T is an independent of {X(t)} non-negative Weibullian random variable. As an illustration, we work out the asymptotics of the supremum distribution of fractional Laplace motion.
Publié le : 2011-02-15
Classification:  exact asymptotics,  fractional Laplace motion,  Gaussian process 
@article{1297173839,
     author = {Arendarczyk, Marek and Debicki, Krzysztof},
     title = {Asymptotics of supremum distribution of a Gaussian process over a Weibullian time},
     journal = {Bernoulli},
     volume = {17},
     number = {1},
     year = {2011},
     pages = { 194-210},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1297173839}
}

Arendarczyk, Marek; Dȩbicki, Krzysztof. Asymptotics of supremum distribution of a Gaussian process over a Weibullian time. Bernoulli, Tome 17 (2011) no. 1, pp.  194-210. http://gdmltest.u-ga.fr/item/1297173839/