Local H\'older regularity for set-indexed processes

Autor:	Herbin, Erick, Richard, Alexandre
Rok vydání:	2012
Předmět:	Mathematics - Probability 60G60 60G17 60G15 60G22 60J65
Druh dokumentu:	Working Paper
Popis:	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 $X_U-X_V$, 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. Comment: 32 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1203.0750 Zobrazit plný text záznamu View this record from Arxiv