Some function spaces associated with Gaussian processes. (Quelques espaces fonctionnels associés à des processus gaussiens.) (French) Zbl 0809.60004

Summary: The first part of the paper presents results on Gaussian measures supported by general Banach sequence spaces and by particular spaces of Besov-Orlicz type. In the second part, a new constructive isomorphism between the just mentioned sequence spaces and corresponding function spaces is established. Consequently, some results on the support function spaces for the Gaussian measure corresponding to the fractional Brownian motion are proved. Next, an application to stochastic equations is given. The last part of the paper contains a result on the support function spaces for stable processes with independent increments.


60B05 Probability measures on topological spaces
60J99 Markov processes
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
41A15 Spline approximation
60G15 Gaussian processes
60G17 Sample path properties
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