Sample path properties of multidimensional integral with respect to stochastic measure

TL;DR

This paper investigates the sample path properties of multidimensional stochastic measure integrals, focusing on their continuity and differentiability under minimal assumptions of sigma-additivity in probability.

Contribution

It establishes the continuity and differentiability of realizations of integrals with respect to multidimensional stochastic measures under weak conditions.

Findings

Proves continuity of the integral's realizations.

Establishes differentiability of the integral's realizations.

Operates under minimal sigma-additivity assumptions.

Abstract

The integral with respect to a multidimensional stochastic measure, for which we assume only $\sigma$-additivity in probability, is studied. The continuity and differentiability of its realizations are established.