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.
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.
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|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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