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Teoriya Veroyatnostei i ee Primeneniya, 1981, Volume 26, Issue 4, Pages 769–783 (Mi tvp3506)  

This article is cited in 34 scientific papers (total in 34 papers)

An asymptotic behaviour of local times of a recurrent random walk with finite variance

A. N. Borodin

Leningrad
Abstract: The paper deals with the asymptotic behaviour (as $n\to\infty$) of the number $\varphi(n,r)$ of times the recurrent random walk $\nu_k$ hits the point $r$ till time $n$. We prove that if the random walk has a finite variance then the processes
$$ t_n(t,x)=n^{-1/2}\varphi([nt],[x\sqrt n]),\qquad(t,x)\in[0,\infty)\times\mathbf R^1 $$
(where $[a]$ is the integer part of $a$), converge weakly to the process $\mathbf t(t,x)$ – the Brownian local time at the point $x$ after time $t$. This result is applied to the investigation of a limit behaviour of a number of processes generated by a recurrent random walk $\nu_k$.
Received: 16.04.1980
English version:
Theory of Probability and its Applications, 1982, Volume 26, Issue 4, Pages 758–772
DOI: https://doi.org/10.1137/1126082
Bibliographic databases:
Language: Russian
Citation: A. N. Borodin, “An asymptotic behaviour of local times of a recurrent random walk with finite variance”, Teor. Veroyatnost. i Primenen., 26:4 (1981), 769–783; Theory Probab. Appl., 26:4 (1982), 758–772
Citation in format AMSBIB
\Bibitem{Bor81}
\by A.~N.~Borodin
\paper An asymptotic behaviour of local times of a~recurrent random walk with finite variance
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 4
\pages 769--783
\mathnet{http://mi.mathnet.ru/tvp3506}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=636771}
\zmath{https://zbmath.org/?q=an:0488.60078|0474.60056}
\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 26
\issue 4
\pages 758--772
\crossref{https://doi.org/10.1137/1126082}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1982PM42700008}
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  • https://www.mathnet.ru/eng/tvp/v26/i4/p769
  • This publication is cited in the following 34 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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