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July, 1992 Sur La Regularite Des Fonctions Aleatoires D'Ornstein-Uhlenbeck A Valeurs Dans lp,p[1,[
X. Fernique
Ann. Probab. 20(3): 1441-1449 (July, 1992). DOI: 10.1214/aop/1176989699

Abstract

In this note, we study the regularity of RN-valued random functions X(Xn,nN) on R such that Xn(t)=anxn(bnt),tR,nN, where a=(an)R+,b=(bn)R+ and (xn,nN) is an i.i.d. sequence of gaussian centered stationary real random functions on R. If the common covariance of the xn's verifies some very weak regularity assumptions, then their paths are continuous in lp,p[1,[ if and only if they are in this space and some integral depending uniquely on p and on a and b is convergent. These results extend and refine some previous results concerning only the case p[2,[.

Citation

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X. Fernique. "Sur La Regularite Des Fonctions Aleatoires D'Ornstein-Uhlenbeck A Valeurs Dans lp,p[1,[." Ann. Probab. 20 (3) 1441 - 1449, July, 1992. https://doi.org/10.1214/aop/1176989699

Information

Published: July, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0759.60036
MathSciNet: MR1175270
Digital Object Identifier: 10.1214/aop/1176989699

Subjects:
Primary: 60G17

Keywords: lp spaces , Ornstein-Uhlenbeck functions , regularity of paths

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 3 • July, 1992
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