A radial invariance principle for nonhomogeneous random walks
Abstract
Consider nonhomogeneous zerodrift 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 $\mathrm{tr}\ \sigma^2 (\mathbf{u}) = V$ in all in directions $\mathbf{u}\in\mathbb{S}^{d1}$ 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2017
 arXiv:
 arXiv:1708.07683
 Bibcode:
 2017arXiv170807683G
 Keywords:

 Mathematics  Probability;
 60J05;
 60F17 (Primary) 60J60 (Secondary)
 EPrint:
 10 pages