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:
https://lup.lub.lu.se/record/4160094
- author
- Basak, Gopal
and Volkov, Stanislav
LU
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Proceedings of the Steklov Institute of Mathematics
- volume
- 282
- issue
- 1
- pages
- 42 - 51
- publisher
- Springer
- 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
- 2016-04-01 13:53:21
- date last changed
- 2022-01-27 21:38:19
@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 = {{Springer}},
series = {{Proceedings of the Steklov Institute of Mathematics}},
title = {{Snakes and perturbed random walks}},
url = {{http://dx.doi.org/10.1134/S0081543813060047}},
doi = {{10.1134/S0081543813060047}},
volume = {{282}},
year = {{2013}},
}