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A note on the simple random walk on Z^2: probability of exiting sequences of sets

Volkov, Stanislav LU orcid (2006) In Statistics and Probability Letters 76(9). p.891-897
Abstract
In this note we establish that the probability that the simple random walk on Z2 returns to its origin before leaving a strip of width L has asymptotically the same probability as the one for hitting the origin before exiting the centered box of the same size. We also generalize this theorem for fairly arbitrary sequences of increasing sets in Z2.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Simple random walk, Hitting probabilities
in
Statistics and Probability Letters
volume
76
issue
9
pages
891 - 897
publisher
Elsevier
external identifiers
  • scopus:33645538581
ISSN
0167-7152
DOI
10.1016/j.spl.2005.10.020
language
English
LU publication?
no
id
2dd1a165-30e6-4dd2-b0be-504ae8497ea1 (old id 4588132)
date added to LUP
2016-04-01 16:39:47
date last changed
2022-01-28 21:17:37
@article{2dd1a165-30e6-4dd2-b0be-504ae8497ea1,
  abstract     = {{In this note we establish that the probability that the simple random walk on Z2 returns to its origin before leaving a strip of width L has asymptotically the same probability as the one for hitting the origin before exiting the centered box of the same size. We also generalize this theorem for fairly arbitrary sequences of increasing sets in Z2.}},
  author       = {{Volkov, Stanislav}},
  issn         = {{0167-7152}},
  keywords     = {{Simple random walk; Hitting probabilities}},
  language     = {{eng}},
  number       = {{9}},
  pages        = {{891--897}},
  publisher    = {{Elsevier}},
  series       = {{Statistics and Probability Letters}},
  title        = {{A note on the simple random walk on Z^2: probability of exiting sequences of sets}},
  url          = {{https://lup.lub.lu.se/search/files/4739529/4588687.pdf}},
  doi          = {{10.1016/j.spl.2005.10.020}},
  volume       = {{76}},
  year         = {{2006}},
}