Geodesic
The It\^{o} integral and the Hitsuda--Skorohod integral in the infinite dimensional case
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 185-199

Voir la notice de l'article provenant de la source Math-Net.Ru

The criterion of adaptedness of a Hilbert space valued stochastic process to the filtration generated by a cylindrical Wiener process is obtained in terms of the S-transform. The criterion is then used to establish the connection between the Itô integral with respect to a cylindrical Wiener process and the Hitsuda–Skhorohod integral in the space of Hilbert space valued stochastic distributions.
Keywords: Itô integral, Hitsuda–Skorohod integral, cylindrical Wiener process
Mots-clés : S-transform. 
@article{SEMR_2014_11_a31,
     author = {M. A. Alshanskiy},
     title = {The {It\^{o}} integral and the {Hitsuda--Skorohod} integral in the infinite dimensional case},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {185--199},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a31/}
}
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M. A. Alshanskiy. The It\^{o} integral and the Hitsuda--Skorohod integral in the infinite dimensional case. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 185-199. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a31/