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 Mat. Tr., 2014, Volume 17, Number 2, Pages 61–83 (Mi mt277)

Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes

I. S. Borisovab, S. E. Khrushchevb

a Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
b Novosibirsk State University, Novosibirsk, 630090, Russia

Abstract: The paper deals with problems of constructing multiple stochastic integrals in the case when the product of increments of the integrating stochastic process admits an expansion as a finite sum of series with random coefficients. This expansion was obtained for a sufficiently wide class including centered Gaussian processes. In the paper, some necessary and sufficient conditions are obtained for the existence of multiple stochastic integrals defined by an expansion of the product of Wiener processes. It was obtained a recurrent representation for the Wiener stochastic integral as an analog of the Hu–Meyer formula.

Key words: multiple stochastic integral multiple Wiener–Itô integral, orthogonal series, expansion of stochastic process, Hu–Meyer formula.

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English version:
Siberian Advances in Mathematics, 2016, 26:1, 1–16

Bibliographic databases:

Document Type: Article
UDC: 519.21

Citation: I. S. Borisov, S. E. Khrushchev, “Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes”, Mat. Tr., 17:2 (2014), 61–83; Siberian Adv. Math., 26:1 (2016), 1–16

Citation in format AMSBIB
\Bibitem{BorKhr14} \by I.~S.~Borisov, S.~E.~Khrushchev \paper Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes \jour Mat. Tr. \yr 2014 \vol 17 \issue 2 \pages 61--83 \mathnet{http://mi.mathnet.ru/mt277} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3330051} \transl \jour Siberian Adv. Math. \yr 2016 \vol 26 \issue 1 \pages 1--16 \crossref{https://doi.org/10.3103/S1055134416010016}