Bernoulli

  • Bernoulli
  • Volume 2, Number 3 (1996), 257-270.

Almost sure oscillation of certain random processes

Jean-Marc Azaïs and Mario Wschebor

Full-text: Open access

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.

Article information

Source
Bernoulli, Volume 2, Number 3 (1996), 257-270.

Dates
First available in Project Euclid: 4 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1178291722

Digital Object Identifier
doi:10.3150/bj/1178291722

Mathematical Reviews number (MathSciNet)
MR1416866

Zentralblatt MATH identifier
0885.60018

Keywords
crossings of a level Gaussian processes martingales occupation measure stable processes

Citation

Azaïs, Jean-Marc; Wschebor, Mario. Almost sure oscillation of certain random processes. Bernoulli 2 (1996), no. 3, 257--270. doi:10.3150/bj/1178291722. https://projecteuclid.org/euclid.bj/1178291722


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