Dr Nicholas Georgiou nicholas.georgiou@durham.ac.uk
Associate Professor
A radial invariance principle for non-homogeneous random walks
Georgiou, Nicholas; Mijatović, Aleksandar; Wade, Andrew R.
Authors
Aleksandar Mijatović
Professor Andrew Wade andrew.wade@durham.ac.uk
Professor
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.
Citation
Georgiou, N., Mijatović, A., & Wade, A. R. (2018). A radial invariance principle for non-homogeneous random walks. Electronic Communications in Probability, 23, Article 56. https://doi.org/10.1214/18-ecp159
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 |
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
This article is available under the terms of Creative Commons Attribution 4.0 International License.
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