Abstract
AbstractWe prove the existence of an intermediate Banach space between the space where the Gaussian measure lives and its RKHS, thus extending what happens with Wiener measure, where the intermediate space can be chosen as a space of Hölder paths. From this result, it is very simple to deduce a result of exponential tightness for Gaussian probabilities.
Funder
Università degli Studi di Roma Tor Vergata
Publisher
Springer Science and Business Media LLC
Reference12 articles.
1. Bergh, J., Löfström J.:Interpolation Spaces. An Introduction, Springer, Berlin-New York, Grundlehren der Mathematischen Wissenschaften, No. 223 (1976)
2. Ciesielski, Z.: On the isomorphisms of the spaces $$H_{\alpha }$$ and $$m$$. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8, 217–222 (1960)
3. de Acosta, A.: Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm. Ann. Probab. 11(1), 78–101 (1983)
4. Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time. III. Commun. Pure Appl. Math. 29(4), 389–461 (1976)
5. Fernique, X.: Intégrabilité des vecteurs gaussiens. C. R. Acad. Sci. Paris Sér. A-B 270, A1698–A1699 (1970)