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Teor. Veroyatnost. i Primenen., 1979, Volume 24, Issue 1, Pages 191–198 (Mi tvp974)  

This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

Conditioned stable random walk with a negative drift

V. I. Afanas'ev

Moscow

Abstract: Let $(S_n, n\ge 0)$ be a random walk with a negative drift, $T=\min\{n\colon S_n\le 0\}$. We prove that if the Cramer's type conditions are satisfied then there exists a constant $\Delta>0$ such that the random functions $S_{[nt]}/ \Delta n^{1/2}$, $0\le t\le 1$ considered under the condition $T>n$, converge weakly to a Brownian excursion when $n\to\infty$.

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English version:
Theory of Probability and its Applications, 1979, 24:1, 192–199

Bibliographic databases:

Received: 23.12.1977

Citation: V. I. Afanas'ev, “Conditioned stable random walk with a negative drift”, Teor. Veroyatnost. i Primenen., 24:1 (1979), 191–198; Theory Probab. Appl., 24:1 (1979), 192–199

Citation in format AMSBIB
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\by V.~I.~Afanas'ev
\paper Conditioned stable random walk with a~negative drift
\jour Teor. Veroyatnost. i Primenen.
\yr 1979
\vol 24
\issue 1
\pages 191--198
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=522253}
\zmath{https://zbmath.org/?q=an:0432.60085|0396.60063}
\transl
\jour Theory Probab. Appl.
\yr 1979
\vol 24
\issue 1
\pages 192--199
\crossref{https://doi.org/10.1137/1124021}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JX60900020}


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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. O. M. Poleshchuk, “The convergence of a conditional random walk to a Brownian bridge”, Russian Math. Surveys, 45:1 (1990), 225–226  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. I. Afanasyev, “On the time of attaining a maximum by a critical branching process in a random environment and by a stopped random walk”, Discrete Math. Appl., 10:3 (2000), 243–264  mathnet  crossref  mathscinet  zmath
    3. V. I. Afanasyev, “On a conditional invariance principle for a critical Galton–Watson branching process”, Discrete Math. Appl., 15:1 (2005), 17–32  mathnet  crossref  crossref  mathscinet  zmath  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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