On the centre of mass of a random walk

Chak Hei Lo and Andrew R. Wade

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 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∑i=1nSi. 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, Gn is 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 Gn is transient in d=1.

Keywords: Random walk; Centre of mass; Barycentre; Time-average; Recurrence classification; Local central limit theorem; Rate of escape (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:11:p:4663-4686

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DOI: 10.1016/j.spa.2018.12.007

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