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February, 1983 Gaussian Measures in $B_p$
Naresh C. Jain, Ditlev Monrad
Ann. Probab. 11(1): 46-57 (February, 1983). DOI: 10.1214/aop/1176993659


For $p \geq 1$, conditions for a separable Gaussian process to have sample paths of finite $p$-variation are given in terms of the mean function and the covariance function. A process with paths of finite $p$-variation may or may not induce a tight measure on the nonseparable Banach space $B_p$. Consequences of tightness and conditions for tightness are given.


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Naresh C. Jain. Ditlev Monrad. "Gaussian Measures in $B_p$." Ann. Probab. 11 (1) 46 - 57, February, 1983.


Published: February, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0504.60045
MathSciNet: MR682800
Digital Object Identifier: 10.1214/aop/1176993659

Primary: 60G15
Secondary: 28C20 , 60B12 , 60G17

Keywords: $p$-variation , ‎Banach spaces , Gaussian , induced measure , nonseparable , sample paths , Stochastic processes , tightness

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • February, 1983
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