Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)



Motions with finite velocity analyzed with order statistics and differential equations

Authors: A. de Gregorio, E. Orsingher and L. Sakhno
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 71 (2004).
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. S. K. Foong and S. Kanno, Properties of the telegrapher's random process with or without a trap, Stochastic Processes and their Applications 53 (1994), 147-173. MR 1290711 (95g:60089)
  • 2. S. Goldstein, On diffusion by discontinuous movements and telegraph equation, Quart. J. Mech. Appl. Math. 4 (1951), 129-156. MR 0047963 (13,960b)
  • 3. S. Leorato and E. Orsingher, Bose-Einstein-type statistics, order statistics and planar random motions with three directions, Advances in Applied Probability 36 (2004), no. 3, 937-970. MR 2079922 (2005g:60171)
  • 4. S. Leorato, E. Orsingher, and M. Scavino, An alternating motion with stops and the related planar, cyclic motion with four directions, Advances in Applied Probability 35 (2003), no. 4, 1153-1168. MR 2014274 (2004g:60132)
  • 5. E. Orsingher, Bessel functions of third order and the distribution of cyclic planar motions with three directions, Stochastics and Stochastics Reports 74 (2002), 617-631. MR 1943582 (2003j:60144)
  • 6. I. V. Samoilenko, Markovian random evolutions in $ R^n$, Random Operators and Stochastic Equations 9 (2001), 139-160. MR 1832161 (2002e:60116)
  • 7. A. F. Turbin and D. N. Plotkin, Bessel equations and functions of higher order, Asymptotic Methods in Problems of Random Evolutions, Institute of Mathematics, Kiev, 1991, pp. 112-121. MR 1190488 (94e:35045)

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60K99, 62G30, 35L25

Retrieve articles in all journals with MSC (2000): 60K99, 62G30, 35L25

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