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Diskr. Mat., 2017, Volume 29, Issue 4, Pages 28–40 (Mi dm1438)  

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

Convergence to the local time of Brownian meander

V. I. Afanasyev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Let $\{ S_{n},\;n\geq 0\}$ be integer-valued random walk with zero drift and variance $\sigma^2$. Let $\xi(k,n)$ be number of $t\in\{1,\ldots,n\}$ such that $S(t)=k$. For the sequence of random processes $\xi(\lfloor u\sigma \sqrt{n}\rfloor,n)$ considered under conditions $S_{1}>0,\ldots ,S_{n}>0$ a functional limit theorem on the convergence to the local time of Brownian meander is proved.

Keywords: Brownian meander, local time of Brownian meander, sojourn time of random walk, functional limit theorems.

DOI: https://doi.org/10.4213/dm1438

Full text: PDF file (467 kB)
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English version:
Discrete Mathematics and Applications, 2019, 29:3, 149–158

Bibliographic databases:

UDC: 519.217.31
Received: 27.06.2017
Revised: 28.10.2017

Citation: V. I. Afanasyev, “Convergence to the local time of Brownian meander”, Diskr. Mat., 29:4 (2017), 28–40; Discrete Math. Appl., 29:3 (2019), 149–158

Citation in format AMSBIB
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\by V.~I.~Afanasyev
\paper Convergence to the local time of Brownian meander
\jour Diskr. Mat.
\yr 2017
\vol 29
\issue 4
\pages 28--40
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\crossref{https://doi.org/10.4213/dm1438}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3781278}
\elib{https://elibrary.ru/item.asp?id=30737795}
\transl
\jour Discrete Math. Appl.
\yr 2019
\vol 29
\issue 3
\pages 149--158
\crossref{https://doi.org/10.1515/dma-2019-0014}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000471785800001}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Afanasyev, “Functional limit theorem for the local time of stopped random walk”, Discrete Math. Appl., 30:3 (2020), 147–157  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. I. Afanasyev, “Two-sided problem for the random walk with bounded maximal increment”, Discrete Math. Appl., 31:2 (2021), 79–89  mathnet  crossref  crossref  mathscinet  isi  elib
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