Mamporia, Badri2018-05-142018-05-142017-04Transactions of A. Razmadze Mathematical Institute 171 (2017) 76–892346-8092doi.org/10.1016/j.trmi.2016.10.003http://hdl.handle.net/123456789/1349Generalized stochastic integral from predictable operator-valued random process with respect to a cylindrical Wiener process in an arbitrary Banach space is defined. The question of existence of the stochastic integral in a Banach space is reduced to the problem of decomposability of the generalized random element. The sufficient condition of existence of the stochastic integral in terms of -absolutely summing operators is given. The stochastic differential equation for generalized random processes is considered and existence and uniqueness of the solution is developed. As a consequence, the corresponding results of the stochastic differential equations in an arbitrary Banach space are givenenIto stochastic integrals and stochastic differential equationsWiener processesCovariance operators in Banach spacesArticle