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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 1, Pages 52–80 (Mi tvp158)  
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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  zmath  isi
    2. I. S. Borisov, S. E. Khrushchev, “Constructing multiple stochastic integrals on non-Gaussian product measures”, Siberian Adv. Math., 24:2 (2014), 75–99  mathnet  crossref  mathscinet  elib
    3. 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  mathnet  crossref  mathscinet
    4. A. A. Bystrov, “Exponential inequalities for probability deviations of stochastic integrals over Gaussian integrable processes”, Theory Probab. Appl., 59:1 (2015), 128–136  mathnet  crossref  crossref  mathscinet  isi  elib
    5. 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  mathnet  crossref  mathscinet
    		• Теория вероятностей и ее применения Theory of Probability and its Applications
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