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Teor. Veroyatnost. i Primenen., 1995, Volume 40, Issue 4, Pages 813–832 (Mi tvp3664)  

This article is cited in 2 scientific papers (total in 2 papers)

A functional limit theorem for random variables with strong residual dependence

O. V. Rusakov

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: To describe a certain model of strongly dependent noise, we introduce the scheme of summation of independent random variables with random replacements. The scheme generates a strictly stationary Markov sequence of random variables. We say that random variables from this sequence have “residual dependence.” In the paper, a Kolmogorov-type inequality for elements of this sequence is given. A functional limit theorem is proved for random polygons generated by these elements. The limiting process turns out to be an Ornstein–Uhlenbeck process.

Keywords: strong dependence, functional limit theorem, Ornstein–Uhlenbeck process, Gaussian noise model.

Full text: PDF file (1259 kB)

English version:
Theory of Probability and its Applications, 1995, 40:4, 714–728

Bibliographic databases:

Received: 15.06.1993

Citation: O. V. Rusakov, “A functional limit theorem for random variables with strong residual dependence”, Teor. Veroyatnost. i Primenen., 40:4 (1995), 813–832; Theory Probab. Appl., 40:4 (1995), 714–728

Citation in format AMSBIB
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\by O.~V.~Rusakov
\paper A functional limit theorem for random variables with strong residual dependence
\jour Teor. Veroyatnost. i Primenen.
\yr 1995
\vol 40
\issue 4
\pages 813--832
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1405147}
\zmath{https://zbmath.org/?q=an:0865.60023}
\transl
\jour Theory Probab. Appl.
\yr 1995
\vol 40
\issue 4
\pages 714--728
\crossref{https://doi.org/10.1137/1140080}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WD22100010}


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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. O. V. Rusakov, A. N. Chuprunov, “Limit theorems for nonhomogeneous Ornstein–Uhlenbeck process”, J. Math. Sci. (N. Y.), 145:2 (2007), 4900–4913  mathnet  crossref  mathscinet  zmath
    2. Khoshnevisan D., Levin D.A., Mendez-Hernandez P.J., “Exceptional times and invariance for dynamical random walks”, Probability Theory and Related Fields, 134:3 (2006), 383–416  crossref  mathscinet  zmath  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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