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 |
|---|---|
| Full text: | Publisher-imposed embargo (AM) Accepted Manuscript File format - PDF (264Kb) |
| Full text: | (VoR) Version of Record Available under License - Creative Commons Attribution. Download PDF (417Kb) |
| 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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