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


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.


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Jean Bertoin. "Sur Une Integrale Pour Les Processus A $\alpha$-Variation Bornee." Ann. Probab. 17 (4) 1521 - 1535, October, 1989.


Published: October, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0687.60054
MathSciNet: MR1048943
Digital Object Identifier: 10.1214/aop/1176991171

Primary: 60H05

Keywords: $\alpha$-variation , Dirichlet process , stochastic integration

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 4 • October, 1989
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