Asymptotic behaviour of non-isotropic random walks with heavy tails
arXiv:1704.02143 · doi:10.15559/17-VMSTA75
Abstract
A random flight on a plane with non-isotropic displacements at the moments of direction changes is considered. In the case of exponentially distributed flight lengths a Gaussian limit theorem is proved for the position of a particle in the scheme of series when jump lengths and non-isotropic displacements tend to zero. If the flight lengths have a folded Cauchy distribution the limiting distribution of the particle position is a convolution of the circular bivariate Cauchy distribution with a Gaussian law.
arXiv commentPublished at http://dx.doi.org/10.15559/17-VMSTA75 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)