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.
Citation
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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