Asymptotic behaviour of non-isotropic random walks with heavy tails
Volume 4, Issue 1 (2017), pp. 79–89
Pub. online: 6 April 2017
Type: Research Article
Open Access
Open Access
Received
24 November 2016
24 November 2016
Revised
9 March 2017
9 March 2017
Accepted
14 March 2017
14 March 2017
Published
6 April 2017
6 April 2017
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.
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