Abstract
In this note, we study the regularity of -valued random functions on such that where and is an i.i.d. sequence of gaussian centered stationary real random functions on . If the common covariance of the 's verifies some very weak regularity assumptions, then their paths are continuous in if and only if they are in this space and some integral depending uniquely on and on and is convergent. These results extend and refine some previous results concerning only the case .
Citation
X. Fernique. "Sur La Regularite Des Fonctions Aleatoires D'Ornstein-Uhlenbeck A Valeurs Dans ." Ann. Probab. 20 (3) 1441 - 1449, July, 1992. https://doi.org/10.1214/aop/1176989699
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