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On the centre of mass of a random walk.

Lo, Chak Hei and Wade, Andrew R. (2019) 'On the centre of mass of a random walk.', Stochastic processes and their applications., 129 (11). pp. 4663-4686.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.spa.2018.12.007
Publisher 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/
Date accepted:04 December 2018
Date deposited:10 December 2018
Date of first online publication:12 December 2018
Date first made open access:12 December 2019

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