Local Hölder regularity for set-indexed processes
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Publication:502988
DOI10.1007/S11856-016-1382-XzbMATH Open1368.60042arXiv1203.0750OpenAlexW2228153092MaRDI QIDQ502988
Author name not available (Why is that?)
Publication date: 11 January 2017
Published in: (Search for Journal in Brave)
Abstract: In this paper, we study the H"older regularity of set-indexed stochastic processes defined in the framework of Ivanoff-Merzbach. The first key result is a Kolmogorov-like H"older-continuity Theorem, whose novelty is illustrated on an example which could not have been treated with anterior tools. Increments for set-indexed processes are usually not simply written as , hence we considered different notions of H"older-continuity. Then, the localization of these properties leads to various definitions of H"older exponents, which we compare to one another. In the case of Gaussian processes, almost sure values are proved for these exponents, uniformly along the sample paths. As an application, the local regularity of the set-indexed fractional Brownian motion is proved to be equal to the Hurst parameter uniformly, with probability one.
Full work available at URL: https://arxiv.org/abs/1203.0750
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