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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

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

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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

Information

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

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

Subjects:
Primary: 60H05

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

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 4 • October, 1989
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