Stochastic integration in Riemannian manifolds from a functional-analytic point of view

Abstract

This article presents a construction of the concept of stochastic integration in Riemannian manifolds from a purely functional-analytic point of view. We show that there are infinitely many such integrals, and that any two of them are related by a simple formula. We also find that the Stratonovich and Itô integrals known to probability theorists are two instances of the general concept constructed herein.

Minor corrections and additions. Final draft, accepted for publication in "Journal of Functional Analysis"