Abstract:
In this paper the construction of a stochastic integral of a nonrandom function is suggested without the classical orthogonality condition of the noise. This construction includes some known constructions of univariate and multiple stochastic integrals. Conditions providing the existence of this integral are specified for noises generated by random processes with nonorthogonal increments from certain classes which are rich enough.
Citation:
I. S. Borisov, A. A. Bystrov, “Constructing a stochastic integral of a nonrandom function without orthogonality of the noise”, Teor. Veroyatnost. i Primenen., 50:1 (2005), 52–80; Theory Probab. Appl., 50:1 (2006), 53–74
\Bibitem{BorBys05}
\by I.~S.~Borisov, A.~A.~Bystrov
\paper Constructing a stochastic integral of a nonrandom function without orthogonality of the noise
\jour Teor. Veroyatnost. i Primenen.
\yr 2005
\vol 50
\issue 1
\pages 52--80
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\crossref{https://doi.org/10.4213/tvp158}
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\zmath{https://zbmath.org/?q=an:1099.60038}
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\transl
\jour Theory Probab. Appl.
\yr 2006
\vol 50
\issue 1
\pages 53--74
\crossref{https://doi.org/10.1137/S0040585X97981469}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000236850700004}
Linking options:
https://www.mathnet.ru/eng/tvp158
https://doi.org/10.4213/tvp158
https://www.mathnet.ru/eng/tvp/v50/i1/p52
This publication is cited in the following 5 articles:
A. A. Bystrov, “Exponential inequalities for probability deviations of stochastic integrals over Gaussian integrable processes”, Theory Probab. Appl., 59:1 (2015), 128–136
I. S. Borisov, S. E. Khrushchev, “Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes”, Siberian Adv. Math., 26:1 (2016), 1–16
I. S. Borisov, V. A. Zhechev, “Invariance principle for canonical $U$- and $V$-statistics based on dependent observations”, Siberian Adv. Math., 25:1 (2015), 21–32
I. S. Borisov, S. E. Khrushchev, “Constructing multiple stochastic integrals on non-Gaussian product measures”, Siberian Adv. Math., 24:2 (2014), 75–99
I. S. Borisov, A. A. Bystrov, “Limit theorems for the canonical von Mises statistics with dependent data”, Siberian Math. J., 47:6 (2006), 980–989
Citation in format AMSBIB
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