Sur Une Integrale Pour Les Processus A $\alpha$-Variation Bornee
Bertoin, Jean
Ann. Probab., Tome 17 (1989) no. 4, p. 1521-1535 / Harvested from Project Euclid
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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.
Publié le : 1989-10-14
Classification:  Stochastic integration,  $\alpha$-variation,  Dirichlet process,  60H05 
@article{1176991171,
     author = {Bertoin, Jean},
     title = {Sur Une Integrale Pour Les Processus A $\alpha$-Variation Bornee},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 1521-1535},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/1176991171}
}

Bertoin, Jean. Sur Une Integrale Pour Les Processus A $\alpha$-Variation Bornee. Ann. Probab., Tome 17 (1989) no. 4, pp.  1521-1535. http://gdmltest.u-ga.fr/item/1176991171/