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Snakes and perturbed random walks

Basak, Gopal and Volkov, Stanislav LU (2013) In Proceedings of the Steklov Institute of Mathematics 282(1). p.42-51
Abstract
We study some properties of random walks perturbed at extrema, which are generalizations of the walks considered, e.g., by Davis (1999) and Tth (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.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Proceedings of the Steklov Institute of Mathematics
volume
282
issue
1
pages
42 - 51
publisher
MAIK Nauka/Interperiodica
external identifiers
  • wos:000325961800004
  • scopus:84886067362
ISSN
0081-5438
DOI
10.1134/S0081543813060047
language
English
LU publication?
yes
id
7449c6af-3993-412d-9694-6f7332cf6694 (old id 4160094)
date added to LUP
2013-12-04 11:37:05
date last changed
2019-02-20 06:03:16
@article{7449c6af-3993-412d-9694-6f7332cf6694,
  abstract     = {We study some properties of random walks perturbed at extrema, which are generalizations of the walks considered, e.g., by Davis (1999) and Tth (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.},
  author       = {Basak, Gopal and Volkov, Stanislav},
  issn         = {0081-5438},
  language     = {eng},
  number       = {1},
  pages        = {42--51},
  publisher    = {MAIK Nauka/Interperiodica},
  series       = {Proceedings of the Steklov Institute of Mathematics},
  title        = {Snakes and perturbed random walks},
  url          = {http://dx.doi.org/10.1134/S0081543813060047},
  volume       = {282},
  year         = {2013},
}