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Transience of continuous-time conservative random walks
- Part of
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- Journal:
- Journal of Applied Probability / Volume 62 / Issue 1 / March 2025
- Published online by Cambridge University Press:
- 18 September 2024, pp. 153-171
- Print publication:
- March 2025
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- Article
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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
$d\ge 2$ and that the rate of direction changing follows a power law 
$t^{-\alpha}$, 
$0<\alpha\le 1$, or the law 
$(\!\ln t)^{-\beta}$ where 
$\beta>2$.
