English

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"