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A radial invariance principle for non-homogeneous random walks

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

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Authors

Aleksandar Mijatović



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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