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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 282, Pages 42–51
DOI: https://doi.org/10.1134/S0371968513030047 (Mi tm3479) 		 
Snakes and perturbed random walks

Gopal Basaka, Stanislav Volkovbc

a Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata, India
b Department of Mathematics, University of Bristol, Bristol, UK
c Centre for Mathematical Sciences, Lund University, Lund, Sweden
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DOI: https://doi.org/10.1134/S0371968513030047
Abstract: We study some properties of random walks perturbed at extrema, which are generalizations of the walks considered, e.g., by Davis (1999) and Tóth (1996). This process can also be viewed as a version of an excited random walk, recently studied by many authors. We obtain several properties related to the range of the process with infinite memory and prove the strong law, the central limit theorem, and the criterion for the recurrence of the perturbed walk with finite memory. We also state some open problems. Our methods are predominantly combinatorial and do not involve complicated analytic techniques.
Received in April 2012
English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 282, Pages 35–44
DOI: https://doi.org/10.1134/S0081543813060047
Bibliographic databases:
Document Type: Article
UDC: 519.217.31
Language: English
Citation: Gopal Basak, Stanislav Volkov, “Snakes and perturbed random walks”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 42–51; Proc. Steklov Inst. Math., 282 (2013), 35–44
Citation in format AMSBIB
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\paper Snakes and perturbed random walks
\inbook Branching processes, random walks, and related problems
\bookinfo Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences
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\yr 2013
\vol 282
\pages 42--51
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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