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This article is cited in 5 scientific papers (total in 5 papers)
Constructing a stochastic integral of a nonrandom function without orthogonality of the noise
I. S. Borisov, A. A. Bystrov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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.
Keywords:
stochastic integral, multiple stochastic integral, noise, Gaussian processes, regular fractional Brownian motion.
DOI:
https://doi.org/10.4213/tvp158
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English version:
Theory of Probability and its Applications, 2006, 50:1, 53–74
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Received: 09.06.2004
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
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/tvp158https://doi.org/10.4213/tvp158 http://mi.mathnet.ru/eng/tvp/v50/i1/p52
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This publication is cited in the following articles:
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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
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I. S. Borisov, S. E. Khrushchev, “Constructing multiple stochastic integrals on non-Gaussian product measures”, Siberian Adv. Math., 24:2 (2014), 75–99
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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
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A. A. Bystrov, “Exponential inequalities for probability deviations of stochastic integrals over Gaussian integrable processes”, Theory Probab. Appl., 59:1 (2015), 128–136
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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
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