An Approach to Stochastic Integration in General Separable Banach Spaces

Abstract

We suggest a new approach to stochastic integration in infinite-dimensional spaces that is based on representing random variables on Banach spaces as real-valued processes on an interval. We prove stochastic integrability of operator-valued processes on general separable Banach spaces under the conditions that do not depend on the norm of the space and show how our methods can be applied to studying infinite-dimensional stochastic differential equations. In particular, our results provide a natural construction of the stochastic integral in abstract Wiener spaces.