A radial invariance principle for non-homogeneous random walks

@article{Georgiou2017ARI,
  title={A radial invariance principle for non-homogeneous random walks},
  author={Nicholas Georgiou and Aleksandar Mijatovi'c and Andrew R. Wade},
  journal={Electronic Communications in Probability},
  year={2017},
  volume={23}
}
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. 
Invariance principle for non-homogeneous random walks
We prove an invariance principle for a class of zero-drift spatially non-homogeneous random walks in $\mathbb{R}^d$, which may be recurrent in any dimension. The limit $\mathcal{X}$ is an ellipticExpand

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