Transport Theorem and Continuity Equations: a Stochastic Approach

TL;DR

This paper introduces a stochastic generalization of the transport theorem on smooth manifolds, deriving a system of continuity equations and demonstrating applications on a torus.

Contribution

It presents a novel stochastic extension of the transport theorem and continuity equations, with specific applications to the torus.

Findings

Derived a stochastic transport theorem on smooth manifolds.

Formulated a system of continuity equations based on the stochastic approach.

Applied the theoretical framework to the case of a torus.

Abstract

We give a stochastic generalization of transport theorem on smooth manifold. Furthermore, we deduce a system of continuity equation and present some application on torus.