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.
Citation
Jean Bertoin. "Sur Une Integrale Pour Les Processus A $\alpha$-Variation Bornee." Ann. Probab. 17 (4) 1521 - 1535, October, 1989. https://doi.org/10.1214/aop/1176991171
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