On Ito Stochastic Integration with Respect to $p$-Stable Motion: Inner Clock, Integrability of Sample Paths, Double and Multiple Integrals
Rosinski, J. ; Woyczynski, W. A.
Ann. Probab., Tome 14 (1986) no. 4, p. 271-286 / Harvested from Project Euclid
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The paper studies in detail the sample paths of Ito-type stochastic integrals with respect to $p$-stable motion $M(t), t \geq 0$. These results, in turn, permit an analysis of the concept of multiple $p$-stable integrals of the form $\int \cdots \int f(t_1,\cdots, t_n)dM(t_1) \cdots dM(t_n)$, and, in particular, a full description of functions of two variables $f(t_1, t_2)$ for which the double stochastic integral $\int \int f(t_1, t_2) dM(t_1) dM(t_2)$ exists.
Publié le : 1986-01-14
Classification:  Ito stochastic integral,  $p$-stable motion,  multiple Wiener-Ito integrals,  60H05,  60G17,  60B11 
@article{1176992627,
     author = {Rosinski, J. and Woyczynski, W. A.},
     title = {On Ito Stochastic Integration with Respect to $p$-Stable Motion: Inner Clock, Integrability of Sample Paths, Double and Multiple Integrals},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 271-286},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992627}
}

Rosinski, J.; Woyczynski, W. A. On Ito Stochastic Integration with Respect to $p$-Stable Motion: Inner Clock, Integrability of Sample Paths, Double and Multiple Integrals. Ann. Probab., Tome 14 (1986) no. 4, pp.  271-286. http://gdmltest.u-ga.fr/item/1176992627/