An alternating motion with stops and the related planar, cyclic motion with four directions
Authors:
- 1 March 2003
- journal article
- general applied-probability
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 35 (04) , 1153-1168
Abstract
In this paper we study a planar random motion (X(t),Y(t)),t>0, with orthogonal directions taken cyclically at Poisson paced times. The process is split into one-dimensional motions with alternating displacements interrupted by exponentially distributed stops. The distributions ofX=X(t) (conditional and nonconditional) are obtained by means of order statistics and the connection with the telegrapher's process is derived and discussed. We are able to prove that the distributions involved in our analysis are solutions of a certain differential system and of the related fourth-order hyperbolic equation.Keywords
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