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Sur une intégrale pour les processus à \(\alpha\)-variation bornée. (On an integral for processes with bounded \(\alpha\)-variation). (French) Zbl 0687.60054

Author’s summary: We define \(\int^{.}_{0}X_ sdY_ s\) for X a process locally of bounded \(\beta\)-variation and Y locally of bounded \(\alpha\)-variation \((\alpha <2\leq \beta\) and \(1/\alpha +1/\beta >1)\) as the limit of the Riemann sums. The properties of this integral lead us to an Itô formula and to the existence of local times for some kinds of Dirichlet processes.
Reviewer: Ching Sung Chou

MSC:

60H05 Stochastic integrals
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