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Theory of Probability and Mathematical Statistics

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Motions with finite velocity analyzed with order statistics and differential equations

Authors: A. de Gregorio, E. Orsingher and L. Sakhno
Journal: Theor. Probability and Math. Statist. 71 (2005), 63-79
MSC (2000): Primary 60K99; Secondary 62G30, 35L25
Published electronically: December 28, 2005
MathSciNet review: 2144321
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Abstract: The aim of this paper is to derive the explicit distribution of the position of randomly moving particles on the line and in the plane (with different velocities taken cyclically) by means of order statistics and by studying suitable problems of differential equations. The two approaches are compared when both are applicable (case of the telegraph process). In some specific cases (alternating motions with skipping) it is possible to use the order statistics approach also to solve the equations governing the distribution. Finally, the approach based on order statistics is also applied in order to obtain the distribution of the position in the case of planar motion with three velocities conditioned on the number of changes of directions recorded.

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Additional Information

A. de Gregorio
Affiliation: Dipartimento di Scienze Statistiche, University of Padua, via Cesare Battisti 241, 35121, Padua, Italy

E. Orsingher
Affiliation: Dipartimento di Statistica, Probabilità e Statistiche Applicate, University of Rome “La Sapienza”, p. le Aldo Moro 5, 00185, Rome, Italy

L. Sakhno
Affiliation: Department of Probability Theory and Mathematical Statistics, Kyiv National Taras Shevchenko University, Volodymyrska 64, 01033, Kyiv, Ukraine

Keywords: Order statistics, Bessel functions of higher order, random motions
Received by editor(s): June 17, 2003
Published electronically: December 28, 2005
Additional Notes: This work was partially supported by the NATO grant PST.CLG.976361.
Article copyright: © Copyright 2005 American Mathematical Society