The Range of Stochastic Integration
Garling, D. J. H.
Ann. Probab., Tome 6 (1978) no. 6, p. 332-334 / Harvested from Project Euclid
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Every measurable real-valued function $f$ on the space of Wiener process paths with $E(|f|^p) < \infty$ (where $0 < p < 1$) can be represented as a stochastic integral $f = \int \varphi dX$, where $E(\int \varphi^2(t)dt)^{p/2} < \infty$. A similar result holds for $1 < p < \infty$ if and only if $E(f) = 0$.
Publié le : 1978-04-14
Classification:  Stochastic integration,  Wiener measure,  60H05 
@article{1176995578,
     author = {Garling, D. J. H.},
     title = {The Range of Stochastic Integration},
     journal = {Ann. Probab.},
     volume = {6},
     number = {6},
     year = {1978},
     pages = { 332-334},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995578}
}

Garling, D. J. H. The Range of Stochastic Integration. Ann. Probab., Tome 6 (1978) no. 6, pp.  332-334. http://gdmltest.u-ga.fr/item/1176995578/