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September 1996 Almost sure oscillation of certain random processes
Jean-Marc Azaïs, Mario Wschebor
Bernoulli 2(3): 257-270 (September 1996). DOI: 10.3150/bj/1178291722

Abstract

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.

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Jean-Marc Azaïs. Mario Wschebor. "Almost sure oscillation of certain random processes." Bernoulli 2 (3) 257 - 270, September 1996. https://doi.org/10.3150/bj/1178291722

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Published: September 1996
First available in Project Euclid: 4 May 2007

zbMATH: 0885.60018
MathSciNet: MR1416866
Digital Object Identifier: 10.3150/bj/1178291722

Keywords: crossings of a level , Gaussian processes , Martingales , occupation measure , Stable processes

Rights: Copyright © 1996 Bernoulli Society for Mathematical Statistics and Probability

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Vol.2 • No. 3 • September 1996
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