Extreme lengths in Brownian and Bessel excursions
Hu, Yueyun ; Shi, Zhan
Bernoulli, Tome 3 (1997) no. 3, p. 387-402 / Harvested from Project Euclid
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We establish some strong limit theorems for the longest excursion lengths of a Bessel process of dimension d ∈ (0,2). In the special case d=1, we recover and improve some well-known results for Wiener processes, and solve an open problem raised. The proof relies on exact distributions evaluated by Pitman and Yor and on a careful analysis of the Bessel sample paths.
Publié le : 1997-12-14
Classification:  Bessel process,  Brownian motion,  excursion length,  Lévy's class 
@article{1175882214,
     author = {Hu, Yueyun and Shi, Zhan},
     title = {Extreme lengths in Brownian and Bessel excursions},
     journal = {Bernoulli},
     volume = {3},
     number = {3},
     year = {1997},
     pages = { 387-402},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175882214}
}

Hu, Yueyun; Shi, Zhan. Extreme lengths in Brownian and Bessel excursions. Bernoulli, Tome 3 (1997) no. 3, pp.  387-402. http://gdmltest.u-ga.fr/item/1175882214/