On the martingale problem for Banach space valued stochastic differential equations (Q1121598)

This paper is concerned with stochastic differential equations with values in a two-smoothable Banach space E. The author first constructs E- valued Gaussian random processes Z(t,x)(\(\cdot)\) which depend in a predictable way on (t,x)\(\in [0,1]\times C([0,1];E)\). The next topic is the construction of a stochastic integral \[ Y_ t=\int^{t}_{0}Z(s,X)(ds) \] for a continuous, adapted E-valued process X. An Itô formula is proved for \(f(X_ t)\). Then, stochastic differential equations are solved and the author discusses the relation between stochastic differential equations and the associated martingale problems.