Invariance principle for non-homogeneous random walks

  title={Invariance principle for non-homogeneous random walks},
  author={Nicholas Georgiou and Aleksandar Mijatovi'c and Andrew R. Wade},
  journal={Electronic Journal of Probability},
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 elliptic martingale diffusion, which may be point-recurrent at the origin for any $d\geq2$. To characterise $\mathcal{X}$, we introduce a (non-Euclidean) Riemannian metric on the unit sphere in $\mathbb{R}^d$ and use it to express a related spherical diffusion as a Brownian motion with drift. This… Expand
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