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

2207.08285Jul 17, 2022Minor corrections and additions. Final draft, accepted for publication in "Journal of Functional Analysis"

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

Alexandru Mustăţea

Functional Analysis Differential Geometry Probability

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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.

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The paper addresses: Stochastic integration in Riemannian manifolds from a functional-analytic point of view.
This article presents a construction of the concept of stochastic integration in Riemannian manifolds from a purely functional-analytic point of view.

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