Quasi Sure p-Variation of Fractional Brownian Sheet

Authors: Guilan Cao ^a; Kai He ^b

Affiliations:	^a Department of Mathematical Sciences, Tsinghua University, Beijing, P.R. China
	^b Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, P.R. China

DOI: 10.1080/07362990600959422

Publication Frequency: 6 issues per year

Published in: journal

Stochastic Analysis and Applications, Volume 24, Issue 6 December 2006 , pages 1223 - 1238

Subjects: Statistics & Probability; Stochastic Models & Processes;

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Abstract

In this article, we prove that for the fractional Brownian sheet B_z with Hurst parameter agr

, β such that agr

+ β > 1, the quasi sure limit of the form $LSAA_A_195850_O_XML_IMAGES\LSAA_A_195850_O_ILM0001.gif$ is zero when $LSAA_A_195850_O_XML_IMAGES\LSAA_A_195850_O_ILM0002.gif$ , where $LSAA_A_195850_O_XML_IMAGES\LSAA_A_195850_O_ILM0003.gif$ , $LSAA_A_195850_O_XML_IMAGES\LSAA_A_195850_O_ILM0004.gif$ , z = (s, t), $LSAA_A_195850_O_XML_IMAGES\LSAA_A_195850_O_ILM0005.gif$ , $LSAA_A_195850_O_XML_IMAGES\LSAA_A_195850_O_ILM0006.gif$ , $LSAA_A_195850_O_XML_IMAGES\LSAA_A_195850_O_ILM0007.gif$ .

Keywords: Fractional Brownian sheet; ∞-modification; p-variation; Quasi sure convergence; (p, agr

)-modification; Sobolev space

Mathematics Subject Classification: 60H07; 60G17

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Quasi Sure p-Variation of Fractional Brownian Sheet

Abstract