A radial invariance principle for non-homogeneous random walks

Georgiou, Nicholas; Mijatović, Aleksandar; Wade, Andrew R.

Abstract

Consider non-homogeneous zero-drift random walks in Rd, d≥2, with the asymptotic increment covariance matrix σ2(u) satisfying u⊤σ2(u)u=U and trσ2(u)=V in all in directions u∈Sd−1 for some positive constants U<V. In this paper we establish weak convergence of the radial component of the walk to a Bessel process with dimension V/U. This can be viewed as an extension of an invariance principle of Lamperti.

• Journal Article Type: Article
• Acceptance Date: Jul 30, 2018
• Online Publication Date: Sep 12, 2018
• Publication Date: Sep 12, 2018
• Deposit Date: Sep 26, 2017
• Publicly Available Date: Sep 13, 2018
• Journal: Electronic Communications in Probability
• Publisher: Bernoulli Society for Mathematical Statistics and Probability
• Peer Reviewed: Peer Reviewed
• Volume: 23
• Article Number: 56
• DOI: https://doi.org/10.1214/18-ecp159
• Public URL: https://durham-repository.worktribe.com/output/1344322