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Transience of continuous-time conservative random walks

Bhattacharya, Satyaki LU and Volkov, Stanislav LU orcid (2025) In Journal of Applied Probability 62(1). p.153-171
Abstract

We consider two continuous-time generalizations of conservative random walks introduced in Englander and Volkov (2022), an orthogonal and a spherically symmetrical one; the latter model is also known as random flights. For both models, we show the transience of the walks when d ≥ 2 and that the rate of direction changing follows a power law t-α, 0 < α ≤ 1, or the law (In t)-β where β ≥ 2.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
conservative random walk, non-time-homogeneous Markov chain, Random flight, recurrence, transience
in
Journal of Applied Probability
volume
62
issue
1
pages
153 - 171
publisher
Applied Probability Trust
external identifiers
  • scopus:85204928214
ISSN
0021-9002
DOI
10.1017/jpr.2024.46
language
English
LU publication?
yes
id
967c2643-ae8a-43bf-bcd5-bdce52de9e30
date added to LUP
2025-01-15 12:16:44
date last changed
2025-10-14 09:30:22
@article{967c2643-ae8a-43bf-bcd5-bdce52de9e30,
  abstract     = {{<p>We consider two continuous-time generalizations of conservative random walks introduced in Englander and Volkov (2022), an orthogonal and a spherically symmetrical one; the latter model is also known as random flights. For both models, we show the transience of the walks when d ≥ 2 and that the rate of direction changing follows a power law t<sup>-α</sup>, 0 &lt; α ≤ 1, or the law (In t)<sup>-β</sup> where β ≥ 2.</p>}},
  author       = {{Bhattacharya, Satyaki and Volkov, Stanislav}},
  issn         = {{0021-9002}},
  keywords     = {{conservative random walk; non-time-homogeneous Markov chain; Random flight; recurrence; transience}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{153--171}},
  publisher    = {{Applied Probability Trust}},
  series       = {{Journal of Applied Probability}},
  title        = {{Transience of continuous-time conservative random walks}},
  url          = {{http://dx.doi.org/10.1017/jpr.2024.46}},
  doi          = {{10.1017/jpr.2024.46}},
  volume       = {{62}},
  year         = {{2025}},
}