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: Dec 12, 2019
• Journal: Stochastic Processes and their Applications
• Print ISSN: 0304-4149
• Electronic ISSN: 1879-209X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 129
• Issue: 11
• Pages: 4663-4686
• DOI: https://doi.org/10.1016/j.spa.2018.12.007
• Public URL: https://durham-repository.worktribe.com/output/1348585