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Sur la régularité de certaines fonctions aléatoires d’Ornstein- Uhlenbeck. (On the regularity of certain Ornstein-Uhlenbeck random processes). (French) Zbl 0706.60041
Necessary and sufficient conditions for the a.s. sample path continuity of a certain class of Ornstein-Uhlenbeck processes (i.e., those for which an associated semigroup of operators is simultaneously diagonalizable) are given. In the special case of $$\ell_ p$$-continuity for separable solutions of the equation $dX=-\Lambda Xdt+\Sigma dW,\quad X(0)=0,$ where $$X(t)\in \ell_ p$$, $$p\geq 2$$, $$\Lambda$$ diagonal $$\Sigma$$ diagonal and non-negative, and W a Wiener process, these conditions are restated in a simpler form. Connections with some problems in the calculus of variations in $$\ell_ p$$ appear in an appendix.
Reviewer: J.Mitro

##### MSC:
 60G15 Gaussian processes 60G17 Sample path properties 60B11 Probability theory on linear topological spaces 49J27 Existence theories for problems in abstract spaces
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