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Random motions in inhomogeneous media


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2008

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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. © 2008 American Mathematical Society.
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Bessel functions , Hyperbolic equations , Poisson process , Rectifying diffeomorphism , Telegraph process
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