The paper is devoted to the construction of stochastic calculus for integrals over martingales measures, including It\ DEGREES{o}, Stratonovich and Skorokhod integrals. We also study multiplicative operator functionals (MOF) in Banach spaces which are a generalization of random evolutions (RE) 2]. One of the results includes Dynkin's formula for MOF. Boundary values problems for RE in Banach spaces are investigated as well. Applications are given to the random evolution