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On the centre of mass of a random walk

Lo, Chak Hei; Wade, Andrew R.

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Authors

Chak Hei Lo



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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