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Random motions governed by third-order equations

Published online by Cambridge University Press:  01 July 2016

Enzo Orsingher
Enzo Orsingher*
Affiliation:
University of Rome ‘La Sapienza'
*
∗Dipartimento di Statistica, Probabilità e Statistiche Applicate, University of Rome ‘La Sapienza’, Piazzale A. Moro 5, 00185 Rome, Italy.
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Abstract

In this paper we analyse the motion of a particle P whose velocity is represented by a three-valued telegraph process. We prove that the probability law of the process describing the position of P is a solution of a third-order, linear, partial differential equation.

We obtain probability distributions of some generalised versions of the process of random signals, as well as other probabilistic features of the related process.

Finally, accelerated motions of P (where acceleration follows the classical telegraph process) are also analysed.

Keywords

TELEGRAPH PROCESSHIGHER-ORDER EQUATIONSACCELERATION
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 4 , December 1990 , pp. 915 - 928
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

This paper was written while the author was at the University of Salerno.

References

Cane, V. (1975) Diffusion models with relativity effects. In Perspectives in Probability and Statistics , ed. Gani, J., distributed by Academic Press for the Applied Probability Trust, Sheffield, 263–273.CrossRefGoogle Scholar
Gardiner, C. W. (1985) Handbook of Stochastic Methods. Springer-Verlag, Berlin.Google Scholar
Orsingher, E. (1990) Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchhoff's laws. Stoch. Proc. Appl. 34, 49–66.Google Scholar