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Teoriya Veroyatnostei i ee Primeneniya, 1994, Volume 39, Issue 4, Pages 681–698 (Mi tvp3847)  
This article is cited in 4 scientific papers (total in 4 papers)

Martingale methods for random walks in a one-dimensional random environment

A. A. Butov

Ulyanovsk State University, Faculty of Mathematics and Mechanics
Full-text PDF (847 kB) Citations (4)
Abstract: One-dimensional random walk processes in a random environment of a general functional type are considered. The study is carried out by the natural scale method. We obtain conditions of existence of the natural scale, conditions of existence of the processes and a theorem on the representation of the local time as the compensator of the modulus of the martingale which is the random walk in the natural scale. The work is performed in martingale terms and contains a number of examples.
Keywords: random walk, random environment, natural scale, semimartingale, compensator.
Received: 06.05.1991
English version:
Theory of Probability and its Applications, 1994, Volume 39, Issue 4, Pages 558–572
DOI: https://doi.org/10.1137/1139043
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. A. Butov, “Martingale methods for random walks in a one-dimensional random environment”, Teor. Veroyatnost. i Primenen., 39:4 (1994), 681–698; Theory Probab. Appl., 39:4 (1994), 558–572
Citation in format AMSBIB
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\by A.~A.~Butov
\paper Martingale methods for random walks in a one-dimensional random environment
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\pages 681--698
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\transl
\jour Theory Probab. Appl.
\yr 1994
\vol 39
\issue 4
\pages 558--572
\crossref{https://doi.org/10.1137/1139043}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TR71500003}
Linking options:
  • https://www.mathnet.ru/eng/tvp3847
  • https://www.mathnet.ru/eng/tvp/v39/i4/p681
    • This publication is cited in the following 4 articles:
    1. A. A. Butov, “Estimating the parameters of distributed productive just-in-time systems”, Autom. Remote Control, 81:3 (2020), 387–397  mathnet  crossref  crossref  isi  elib
    2. A. A. Butov, A. A. Kovalenko, “Stochastic models of just-in-time systems and windows of vulnerability in terms of the processes of birth and death”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:3 (2019), 525–540  mathnet  crossref
    3. A. A. Butov, A. A. Kovalenko, “Stochastic models of simple controlled systems just-in-time”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:3 (2018), 518–531  mathnet  crossref  elib
    4. Alexander A. Butov, “On the problem of optimal instant observations of the linear birth and death process”, Statistics & Probability Letters, 101 (2015), 49  crossref
    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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