Summary
Existence and continuity of Ornstein-Uhlenbeck processes in Banach and Hilbert spaces are investigated under various assumptions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Antoniadis, A., Carmona, R.: Eigenfunction expansions for infinite dimensional Ornstein-Uhlenbeck processes. Probab. Theory Relat. Fields74, 31–54 (1987)
Badrikian, A., Chevet, S.: Mesure cylindrique, espaces de Wiener et fonctions aléatoires gaussiennes. (Lect. Notes Math., vol. 379) Berlin Heidelberg New York: Springer 1974
Carmona, R.: Tensor products of Gaussian measures. In: Proc. Conf. Vector Space Measures and Appli. Dublin 1977. (Lect. Notes Math., vol. 644, pp. 96–124) Berlin Heidelberg New York: Springer 1978
Chojnowska-Michalik, A.: Stochastic differential equations in Hilbert spaces. (Banach Cent. Publ., vol. 5 Probability Theory, pp. 53–74) Warsawa: PWN 1979
da Prato, G., Kwapień, S., Zabczyk J: Regularity of solutions of linear stochastic equations in Hilbert spaces. Stochastics23, 1–23 (1987)
da Prato, G., Sinestrari, E.: Differential operators with non dense domain. Ann. Sc. Norm. Super. Pisa, Cl. Sci. IV.14, 285–344 (1988)
Dawson, D.A.: Stochastic evolution equations. Math. Biosci.15, 287–316 (1972)
Dellacherie, C., Meyer, P.A.: Probabilités et potentiels, chaps. 1–4. Paris: Hermann 1975
de Simon, L.: Un Applicazione della teoria degli integrali signorali allo studio delle equazioni differenziali lineari astrate del primo ordine. Rend. Semin. Mat. Univ. Padova34, 205–223 (1964)
Fernique, X.: La régularité des fonctions aléatoires d'Ornstein-Uhlenbeck à valeurs dansl 2; le cas diagonal. C.R. Acad. Sci., Paris, Sér. I309, 59–62 (1989)
Fernique, X.: Fonctions aléatoires dans les espaces Lusiniens. Expo. Math.8, 289–364 (1990)
Fernique, X.: Régularité de fonctions aléatoires gaussiennes en dimension infinie. (Preprint 1990)
Henry, D.: Geometric theory of semilinear parabolic equations. (Lect. Notes Math., vol. 840) Berlin Heidelberg New York: Springer 1981
Hille, E., Phillips, R.S.: Functional analysis and semigroups. Coll. Publ. Am. Math. Soc. vol. 31) Providence RI: Am. Math. Soc. 1957
Iscoe, I., Mc Donald, D.: Continuity ofl 2-valued Ornstein-Uhlenbeck processes. Technical Report of the Carleton University 1986
Iscoe, I., Marcus, M.B., Mc Donald, D., Talagrand, M., Zinn, J.: Continuity ofl 2-valued Ornstein-Uhlenbeck processes. Ann. Probab.18, 68–84 (1990)
Kotelenez, P.: A maximal inequality for stochastic convolution integrals on Hilbert spaces and space-time regularity of linear stochastic partial differential equations. Stochastics21, 328–345 (1987)
Krein, S.G.: Linear differential equations in Banach spaces. (Transl. Math. Monogr., vol. 29) Providence, RI: Am. Math. Soc. 1971
Kuo, H.H.: Gaussian measures in Banach spaces. (Lect. Notes Math., vol. 463) Berlin Heidelberg New York: Springer 1975
Sinestrari, E.: On the abstract Cauchy problem of parabolic type in spaces of continuous functions. J. Math. Anal. Appl.107, 16–66 (1985)
Smoleński, W.H.: Continuity of Ornstein-Uhlenbeck processes. Bull. Pol. Acad. Sci.37, 203–206 (1989)
Smoleński, W., Sztencel, R., Zabczyk, J.: Large deviations estimates for semi-linear equations. In: Englebert, H.J., Schmidt, W. (eds.) Proceedings of the 5th IFIP Conference on Stochastic Differential Systems. Eisenach 1986. (Lect. Notes Control Inf. Sci., vol. 96, pp. 218–231) Berlin Heidelberg New York: Springer 1987
Author information
Authors and Affiliations
Additional information
This work was partly written when W. Smoleński visited the Mathematics Department in Angers
Rights and permissions
About this article
Cite this article
Millet, A., Smoleński, W. On the continuity of Ornstein-Uhlenbeck processes in infinite dimensions. Probab. Th. Rel. Fields 92, 529–547 (1992). https://doi.org/10.1007/BF01274267
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01274267