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