A radial invariance principle for non-homogeneous random walks

  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},
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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