Stochastic Calculus in Separable Banach Spaces
This chapter is devoted to the development of stochastic calculus in separable Banach spaces, including construction of integrals over martingale measures, such as Ito, Stratonovich and Skorokhod integrals. It studies multiplicative operator functionals (MOF) in Banach spaces, which are a generalization of random evolutions. The chapter investigates boundary values problems for MOF in Banach spaces and provides applications to the evolutionary stochastic systems. It derives equations for resolvent and potential of MOF of Markov processes and considers an analogue of Dynkin’s formula for MOF of Markov processes. The applications of Dynkin’s formula to traffic, storage and diffusion processes in random media are also discussed.