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IMI/Publicaţii/BASM/Ediţii/BASM n.2 (45), 2004/

Cyclic planar random evolution with four directions.

Authors: Kolesnik Alexander

Abstract

A four-direction cyclic random motion with constant finite speed v in the plane R2 driven by a homogeneous Poisson process of rate lambda > 0 is studied. A fourth-order hyperbolic equation with constant coefficients governing the transition law of the motion is obtained. A general solution of the Fourier transform of this equation is given. A special non-linear automodel substitution is found reducing the governing partial differential equation to the generalized fourth-order ordinary Bessel differential equation, and the fundamental system of its solutions is explicitly given.

Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
5 Academiei str. Chisinau,
MD-2028 Moldova
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