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

Authors
  • Borisov, I. S.1, 2
  • Khrushchev, S. E.2
  • 1 Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia , Novosibirsk (Russia)
  • 2 Novosibirsk State University, Novosibirsk, 630090, Russia , Novosibirsk (Russia)
Type
Published Article
Journal
Siberian Advances in Mathematics
Publisher
Allerton Press
Publication Date
Jan 01, 2016
Volume
26
Issue
1
Pages
1–16
Identifiers
DOI: 10.3103/S1055134416010016
Source
Springer Nature
Keywords
License
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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.

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