Random motions in inhomogeneous media

Orsingher, E.; Ratanov, N.

doi:10.1090/S0094-9000-08-00738-2

Random motions in inhomogeneous media

Authors: E. Orsingher and N. E. Ratanov
Translated by: The authors
Journal: Theor. Probability and Math. Statist. 76 (2008), 141-153
MSC (2000): Primary 60K99; Secondary 62G30, 35L25, 60C05
DOI: https://doi.org/10.1090/S0094-9000-08-00738-2
Published electronically: July 16, 2008
MathSciNet review: 2368746
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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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