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An alternating motion with stops and the related planar, cyclic motion with four directions

Part of: Special processes Hyperbolic equations and systems Nonparametric inference

Published online by Cambridge University Press:  01 July 2016

S. Leorato ,
E. Orsingher  and
M. Scavino
S. Leorato*
Affiliation:
University of Rome ‘La Sapienza’
E. Orsingher*
Affiliation:
University of Rome ‘La Sapienza’
M. Scavino*
Affiliation:
Universidad de la República, Montevideo
*
∗ Postal address: Dipartimento di Statistica, Probabilità e Statistiche Applicate, University of Rome ‘La Sapienza’, Piazzale Aldo Moro, 5, 00185 Rome, Italy.
∗ Postal address: Dipartimento di Statistica, Probabilità e Statistiche Applicate, University of Rome ‘La Sapienza’, Piazzale Aldo Moro, 5, 00185 Rome, Italy.
∗∗∗ Postal address: Universidad de la República, Facultad de Ciencias Económicas y de Administración, Instituto de Estadística, Eduardo Acevedo 1139, 11200 Montevideo, Uruguay.
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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 of X = 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

Order statisticshypergeometric functiontelegrapher's processrandom motionexchangeabilityhyperbolic equation

MSC classification

Primary: 60K99: None of the above, but in this section
Secondary: 62G30: Order statistics; empirical distribution functions 35L25: Higher-order hyperbolic equations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 4 , December 2003 , pp. 1153 - 1168
Copyright
Copyright © Applied Probability Trust 2003 

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References

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