Stochastic integration in Riemannian manifolds from a functional-analytic point of view
Functional Analysis
2023-06-01 v2 Differential Geometry
Probability
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 It\^o integrals known to probability theorists are two instances of the general concept constructed herein.
Keywords
Cite
@article{arxiv.2207.08285,
title = {Stochastic integration in Riemannian manifolds from a functional-analytic point of view},
author = {Alexandru Mustăţea},
journal= {arXiv preprint arXiv:2207.08285},
year = {2023}
}
Comments
Minor corrections and additions. Final draft, accepted for publication in "Journal of Functional Analysis"