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Teoriya Veroyatnostei i ee Primeneniya, 1979, Volume 24, Issue 1, Pages 191–198 (Mi tvp974)  

This article is cited in 7 scientific papers (total in 7 papers)

Short Communications

Conditioned stable random walk with a negative drift

V. I. Afanas'ev

Moscow
Full-text PDF (504 kB) Citations (7)
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 $n\to\infty$.
Received: 23.12.1977
English version:
Theory of Probability and its Applications, 1979, Volume 24, Issue 1, Pages 192–199
DOI: https://doi.org/10.1137/1124021
Bibliographic databases:
Document Type: Article
Language: Russian
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://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JX60900020}
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  • https://www.mathnet.ru/eng/tvp/v24/i1/p191
  • This publication is cited in the following 7 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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