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Main Title: Propagation of Singularities in the Semi-Fractional Brownian Sheet
Author(s): Blath, Jochen
Martin, Andreas
Type: Research Paper
Abstract: Let $X$ be a semi-fractional Brownian sheet, that is a centred and continuous Gaussian random field with $\mathbb E [X(s,t)X(\hat{s},\hat{t}\,)] = (t\wedge \hat{t}\,) (s^\alpha + \hat{s}^\alpha-|s-\hat{s}|^\alpha)/2$. We provide, for $\alpha\in(0,2)$, an analysis of the propagation of singularities into the fractional direction of $X$. Here, singularities are times where the law of the iterated logarithm fails, such as fast points.
Subject(s): propagation of singularities
fractional Brownian motion
semi-fractional Brownian sheet
Gaussian random field
fast points
Issue Date: 28-Nov-2006
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 60G15 Gaussian processes
60G17 Sample path properties
60G60 Random fields
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2006, 25
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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