Une construction d'une int\'egrale relativement \`a un processus al\'eatoire

TL;DR

This paper extends the concept of iterated integrals to unpredictable processes, providing a formula for integration by parts, establishing the existence of continuous modifications, and expressing the increasing process.

Contribution

It introduces a generalized framework for iterated integrals with respect to unpredictable processes, including new formulas and existence results.

Findings

Derived a formula of integration by parts for unpredictable processes

Proved the existence of continuous modifications of the integrals

Expressed the increasing process associated with the integral

Abstract

In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.