Theory of Probability and Mathematical Statistics

Motions with finite velocity analyzed with order statistics and differential equations

Author(s): A. de Gregorio; E. Orsingher; L. Sakhno
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, vipusk 71 (2004).
Journal: Theor. Probability and Math. Statist. No. 71 (2005), 63-79.
MSC (2000): Primary 60K99; Secondary 62G30, 35L25
Posted: December 28, 2005
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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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Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60K99, 62G30, 35L25

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
Email: enzo.orsingher@uniroma1.it

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

DOI: 10.1090/S0094-9000-05-00648-4
PII: S 0094-9000(05)00648-4
Keywords: Order statistics, Bessel functions of higher order, random motions
Received by editor(s): 17/JUN/2003
Posted: December 28, 2005
Additional Notes: This work was partially supported by the NATO grant PST.CLG.976361.
Copyright of article: Copyright 2005, American Mathematical Society

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ISSN: 1547-7363(e) 0094-9000(p)

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