Almost sure oscillation of certain random processes
Azaïs, Jean-Marc ; Wschebor, Mario
Bernoulli, Tome 2 (1996) no. 3, p. 257-270 / Harvested from Project Euclid
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We show that for various classes of stochastic process, namely Gaussian processes, stable Lévy processes and Brownian martingales, we have almost sure weak convergence of the oscillation in the measure space ([0,1],λ), λ being Lebesgue measure. This result is used to obtain almost sure weak approximation of the occupation measure via numbers of crossings.
Publié le : 1996-09-14
Classification:  crossings of a level,  Gaussian processes,  martingales,  occupation measure,  stable processes 
@article{1178291722,
     author = {Aza\"\i s, Jean-Marc and Wschebor, Mario},
     title = {Almost sure oscillation of certain random processes},
     journal = {Bernoulli},
     volume = {2},
     number = {3},
     year = {1996},
     pages = { 257-270},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1178291722}
}

Azaïs, Jean-Marc; Wschebor, Mario. Almost sure oscillation of certain random processes. Bernoulli, Tome 2 (1996) no. 3, pp.  257-270. http://gdmltest.u-ga.fr/item/1178291722/