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Sib. Èlektron. Mat. Izv., 2014, Volume 11, Pages 185–199 (Mi semr479)  

This article is cited in 2 scientific papers (total in 2 papers)

Probability theory and mathematical statistics

The Itô integral and the Hitsuda–Skorohod integral in the infinite dimensional case

M. A. Alshanskiy

Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: 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, S-transform.

Full text: PDF file (611 kB)
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Document Type: Article
UDC: 519.21
MSC: 46F25, 60H05, 60H40
Received September 19, 2013, published March 2, 2014

Citation: M. A. Alshanskiy, “The Itô integral and the Hitsuda–Skorohod integral in the infinite dimensional case”, Sib. Èlektron. Mat. Izv., 11 (2014), 185–199

Citation in format AMSBIB
\Bibitem{Als14}
\by M.~A.~Alshanskiy
\paper The It\^{o} integral and the Hitsuda--Skorohod integral in the infinite dimensional case
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 185--199
\mathnet{http://mi.mathnet.ru/semr479}


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    This publication is cited in the following articles:
    1. O. S. Starkova, “Slaboe i obobschennoe po sluchainoi peremennoi resheniya stokhasticheskoi zadachi Koshi s additivnym shumom”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 8:1 (2016), 19–27  mathnet  crossref  elib
    2. I. V. Melnikova, M. A. Alshanskiy, “Stochastic equations with an unbounded operator coefficient and multiplicative noise”, Siberian Math. J., 58:6 (2017), 1052–1066  mathnet  crossref  crossref  isi  elib
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