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A radial invariance principle for non-homogeneous random walks.

Georgiou, Nicholas and Mijatović, Aleksandar and Wade, Andrew R. (2018) 'A radial invariance principle for non-homogeneous random walks.', Electronic communications in probability., 23 . p. 56.

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.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1214/18-ecp159
Publisher statement:This article is available under the terms of Creative Commons Attribution 4.0 International License.
Date accepted:30 July 2018
Date deposited:31 July 2018
Date of first online publication:12 September 2018
Date first made open access:No date available

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