Transport equation driven by a stochastic measure

TL;DR

This paper investigates a stochastic transport equation driven by a stochastic measure, establishing the existence and uniqueness of weak solutions under minimal assumptions on the measure's properties.

Contribution

It introduces a framework for solving the stochastic transport equation driven by a stochastic measure with minimal regularity assumptions.

Findings

Proved existence of weak solutions.

Established uniqueness of solutions.

Extended the theory to measures with only $\sigma$-additivity and path continuity.

Abstract

We consider the stochastic transport equation where the randomness is given by the symmetric integral with respect to stochastic measure. For stochastic measure, we assume only $\sigma$-additivity in probability and continuity of paths. The existence and uniqueness of the weak solution to the equation are proved.