Chak Hei Lo
On the centre of mass of a random walk
Lo, Chak Hei; Wade, Andrew R.
Abstract
For a random walk Sn on Rd we study the asymptotic behaviour of the associated centre of mass process Gn=n−1∑ni=1Si. For lattice distributions we give conditions for a local limit theorem to hold. We prove that if the increments of the walk have zero mean and finite second moment, Gnis recurrent if d=1 and transient if d≥2. In the transient case we show that Gn has a diffusive rate of escape. These results extend work of Grill, who considered simple symmetric random walk. We also give a class of random walks with symmetric heavy-tailed increments for which Gnis transient ind=1.
Citation
Lo, C. H., & Wade, A. R. (2019). On the centre of mass of a random walk. Stochastic Processes and their Applications, 129(11), 4663-4686. https://doi.org/10.1016/j.spa.2018.12.007
Journal Article Type | Article |
---|---|
Acceptance Date | Dec 4, 2018 |
Online Publication Date | Dec 12, 2018 |
Publication Date | Nov 30, 2019 |
Deposit Date | Sep 26, 2017 |
Publicly Available Date | Mar 28, 2024 |
Journal | Stochastic Processes and their Applications |
Print ISSN | 0304-4149 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 129 |
Issue | 11 |
Pages | 4663-4686 |
DOI | https://doi.org/10.1016/j.spa.2018.12.007 |
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Copyright Statement
© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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