Stochastic differential equation driven by the Wiener process in a Banach space, existence and uniqueness of the generalized solution
Pure and Applied Mathematics Journal
Volume 4, Issue 3, June 2015, Pages: 133-138
Received: Dec. 15, 2014;
Accepted: Dec. 16, 2014;
Published: Jun. 11, 2015
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Badri Mamporia, Niko Muskhelishvili Institute of Computational Mathematics, Technical University of Georgia, Tbilisi, Georgia
In this paper the stochastic differential equation in a Banach space is considered for the case when the Wiener process in the equation is Banach space valued and the integrand non-anticipating function is operator-valued. At first the stochastic differential equation for the generalized random process is introduced and developed existence and uniqueness of solutions as the generalized random process. The corresponding results for the stochastic differential equation in a Banach space is given. In  we consider the stochastic differential equation in a Banach space in the case, when the Wiener process is one dimensional and the integrand non-anticipating function is Banach space valued.
Stochastic differential equation driven by the Wiener process in a Banach space, existence and uniqueness of the generalized solution, Pure and Applied Mathematics Journal.
Vol. 4, No. 3,
2015, pp. 133-138.
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