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Teoriya Veroyatnostei i ee Primeneniya, 1979, Volume 24, Issue 4, Pages 754–770 (Mi tvp2895)  

This article is cited in 1 scientific paper (total in 1 paper)

Some limit theorems for the processes with random time

A. N. Borodin

Leningrad
Full-text PDF (952 kB) Citations (1)
Abstract: Suppose that $G(t,\omega)$ and $F(t,\omega)$ are independent stochastic processes satisfying Rosenblatt's mixing condition (0.3). We consider the processes with random time $Q(t,\omega)=G(H(t),\omega)$, where the function $H(t)$ in the case of continuous $t$ is defined by (0.8) and in the case of discrete $t$ – by (0.9). The weak convergence of the process
$$ Z_{\varepsilon}(\tau)=\varepsilon^{1/2}\int_0^{\tau/\varepsilon}G(H(t),\omega)\,dt\qquad(0\le\tau\le 1) $$
to the process $\sqrt{V(\omega)}W(\tau)$ is proved. Here $V(\omega)$ is defined by (3.2) and $W(\tau)$ is a Wiener process independent of the random variable $V(\omega)$. A stochastic approximation procedure for the processes with random time is discussed also.
Received: 05.05.1977
English version:
Theory of Probability and its Applications, 1980, Volume 24, Issue 4, Pages 755–771
DOI: https://doi.org/10.1137/1124088
Bibliographic databases:
Language: Russian
Citation: A. N. Borodin, “Some limit theorems for the processes with random time”, Teor. Veroyatnost. i Primenen., 24:4 (1979), 754–770; Theory Probab. Appl., 24:4 (1980), 755–771
Citation in format AMSBIB
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\by A.~N.~Borodin
\paper Some limit theorems for the processes with random time
\jour Teor. Veroyatnost. i Primenen.
\yr 1979
\vol 24
\issue 4
\pages 754--770
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\zmath{https://zbmath.org/?q=an:0441.60034|0417.60046}
\transl
\jour Theory Probab. Appl.
\yr 1980
\vol 24
\issue 4
\pages 755--771
\crossref{https://doi.org/10.1137/1124088}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979KW11900006}
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  • https://www.mathnet.ru/eng/tvp/v24/i4/p754
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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