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August, 1982 On the Existence of Natural Rate of Escape Functions for Infinite Dimensional Brownian Motions
Dennis D. Cox
Ann. Probab. 10(3): 623-638 (August, 1982). DOI: 10.1214/aop/1176993772

Abstract

It is proved that genuinely infinite dimensional Brownian motions on $\ell^p$ sequence spaces have natural rates of escape, provided the coordinates are independent. An analogous result holds for separable Hilbert space. Computations of Brownian rates of escape and further properties are considered.

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Dennis D. Cox. "On the Existence of Natural Rate of Escape Functions for Infinite Dimensional Brownian Motions." Ann. Probab. 10 (3) 623 - 638, August, 1982. https://doi.org/10.1214/aop/1176993772

Information

Published: August, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0493.60048
MathSciNet: MR659533
Digital Object Identifier: 10.1214/aop/1176993772

Subjects:
Primary: 60G15
Secondary: 39C05 , 60B05 , 60B12 , 60G17

Keywords: Brownian motion in a Banach space , functional inequality problem , infinitely many dimensions , log concavity , natural rate of escape

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 3 • August, 1982
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