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2018 A radial invariance principle for non-homogeneous random walks
Nicholas Georgiou, Aleksandar Mijatović, Andrew R. Wade
Electron. Commun. Probab. 23: 1-11 (2018). DOI: 10.1214/18-ECP159

Abstract

Consider non-homogeneous zero-drift random walks in $\mathbb{R} ^d$, $d \geq 2$, with the asymptotic increment covariance matrix $\sigma ^2 (\mathbf{u} )$ satisfying $\mathbf{u} ^{\top } \sigma ^2 (\mathbf{u} ) \mathbf{u} = U$ and $\operatorname{tr} \sigma ^2 (\mathbf{u} ) = V$ in all in directions $\mathbf{u} \in \mathbb{S} ^{d-1}$ 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.

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Nicholas Georgiou. Aleksandar Mijatović. Andrew R. Wade. "A radial invariance principle for non-homogeneous random walks." Electron. Commun. Probab. 23 1 - 11, 2018. https://doi.org/10.1214/18-ECP159

Information

Received: 25 August 2017; Accepted: 30 July 2018; Published: 2018
First available in Project Euclid: 12 September 2018

zbMATH: 1401.60133
MathSciNet: MR3863912
Digital Object Identifier: 10.1214/18-ECP159

Subjects:
Primary: 60F17, 60J05
Secondary: 60J60

JOURNAL ARTICLE
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