Une g\'en\'eralisation de la notion d'int\'egrale it\'er\'ee relativement \`a un processus al\'eatoire

TL;DR

This paper extends the concept of iterated integrals to unpredictable processes, providing new formulas, existence results, and expressions for associated increasing processes.

Contribution

It introduces a generalized framework for iterated integrals with respect to unpredictable processes, including integration by parts and continuity properties.

Findings

Established a formula of integration by parts.

Proved the existence of a continuous modification.

Derived an expression for the increasing process.

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.