On the centre of mass of a random walk

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Lo, Chak Hei¹  Wade, Andrew R.¹ 

[1] Univ Durham, Dept Math Sci, South Rd, Durham DH1 3LE, England

关键词: Random walk;    Centre of mass;    Barycentre;    Time-average;    Recurrence classification;    Local central limit theorem;    Rate of escape;   

DOI  :  10.1016/j.spa.2018.12.007

来源: Elsevier

【 摘 要 】

For a random walk S-n on R-d we study the asymptotic behaviour of the associated centre of mass process G(n) = n(-1) Sigma(n)(i=1) S-i. 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, G(n) is recurrent if d = 1 and transient if d >= 2. In the transient case we show that G(n) 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 G(n) is transient in d = 1. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free