Theory of Probability and Mathematical Statistics

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



Random motions in inhomogeneous media

Authors: E. Orsingher and N. E. Ratanov
Translated by: The authors
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 76 (2007).
Journal: Theor. Probability and Math. Statist. 76 (2008), 141-153
MSC (2000): Primary 60K99; Secondary 62G30, 35L25, 60C05
Published electronically: July 16, 2008
MathSciNet review: 2368746
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Abstract | References | Similar Articles | Additional Information

Abstract: Space inhomogeneous random motions of particles on the line and in the plane are considered in the paper. The changes of the movement direction are driven by a Poisson process. The particles are assumed to move according to a finite velocity field that depends on a spatial argument.

The explicit distribution of particles is obtained in the paper for the case of dimension 1 in terms of characteristics of the governing equations. In the case of dimension 2, the distribution is obtained if a rectifying diffeomorphism exists.

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Additional Information

E. Orsingher
Affiliation: Dipartimento di Statistica, Probabilitá e Statistiche Applicate, Universitá degli Studi di Roma “La Sapienza”, 00185 Rome, Italy

N. E. Ratanov
Affiliation: Universidad del Rosario, Bogotá, Colombia

Keywords: Bessel functions, Poisson process, rectifying diffeomorphism, hyperbolic equations, telegraph process
Received by editor(s): May 16, 2006
Published electronically: July 16, 2008
Article copyright: © Copyright 2008 American Mathematical Society