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The paper is devoted to the construction of stochastic calculus for integrals over martingales measures, including It\^{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 evolutions.

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Anatoliy Swishchuk is a Professor of mathematical finance at the University of Calgary, Canada. His research interests include modelling and pricing swaps, weather and energy derivatives, option pricing, regime-switching models, random evolutions and their applications. He is the author of many research papers and 10 books.

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