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Статья

Asymptotic behaviour of non-isotropic random walks with heavy tails

Modern Stochastics: Theory and Applications. 2017. Vol. 1. No. 4. P. 79-89.
Kelbert M., Orsingher E.

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.