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July 2003 On the sample paths of Brownian motions on compact infinite dimensional groups
Alexander Bendikov, Laurent Saloff-Coste
Ann. Probab. 31(3): 1464-1493 (July 2003). DOI: 10.1214/aop/1055425787

Abstract

We study the regularity of the sample paths of certain Brownian motions on the infinite dimensional torus ${\mathbb T}^\infty$ and other compact connected groups in terms of the associated intrinsic distance. For each $\lambda\in (0,1)$, we give examples where the intrinsic distance $d$ is continuous and defines the topology of ${\mathbb T}^\infty$ and where the sample paths satisfy \[ 0<\liminf_{t\ra 0} \frac{d(X_0,X_t)}{t^{(1-\lambda)/2}}\le \limsup_{t\ra 0} \frac{d(X_0,X_t)}{t^{(1-\lambda)/2}}<\infty \] and \[ 0<\lim_{\varepsilon\to 0} \sup_{0<t<s<1 \atop t-s\le \varepsilon}\frac{d(X_s,X_t)}{(t-s )^{(1-\lambda)/2}} <\infty. \]

Citation

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Alexander Bendikov. Laurent Saloff-Coste. "On the sample paths of Brownian motions on compact infinite dimensional groups." Ann. Probab. 31 (3) 1464 - 1493, July 2003. https://doi.org/10.1214/aop/1055425787

Information

Published: July 2003
First available in Project Euclid: 12 June 2003

zbMATH: 1043.60064
MathSciNet: MR1989440
Digital Object Identifier: 10.1214/aop/1055425787

Subjects:
Primary: 31C25, 47D07, 60B99, 60J60

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 3 • July 2003
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