Sur Une Integrale Pour Les Processus A $\alpha$-Variation Bornee

Abstract

We define $\int^\bullet_0 X_s dY_s$ for $X$ a process locally of bounded $\beta$-variation and $Y$ locally of bounded $\alpha$-variation $(\alpha < 2 \leq \beta \text{and} 1/\alpha + 1/\beta > 1)$ as the limit of the Riemann sums. The properties of this integral lead us to an Ito formula and to the existence of local times for some kinds of Dirichlet processes.