Wiener-Itô Chaos Expansion of Hilbert Space Valued Random Variables. (7th April 2014)

• Record Type: Journal Article
• Authors: Alshanskiy, M. A.
• Other Names: Mukhamedov Farrukh Academic Editor.
• Is Part Of: Journal of probability. Volume 2014(2014)
• Publication Date: 2014-04-07
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519.2
• DOI: 10.1155/2014/786854
• Languages: English
• ISSNs: 2356-7589

Abstract

Abstract : The notion ofn -fold iterated Itô integral with respect to a cylindrical Hilbert space valued Wiener process is introduced and the Wiener-Itô chaos expansion is obtained for a square Bochner integrable Hilbert space valued random variable. The expansion can serve a basis for developing the Hilbert space valued analog of Malliavin calculus of variations which can then be applied to the study of stochastic differential equations in Hilbert spaces and their solutions.