Geodesic
Cyclic planar random evolution with four directions
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2004), pp. 27-32

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A four-direction cyclic random motion with constant finite speed $v$ in the plane $R^2$ 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. 
@article{BASM_2004_2_a2,
     author = {Alexander D. Kolesnik},
     title = {Cyclic planar random evolution with four directions},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {27--32},
     publisher = {mathdoc},
     number = {2},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2004_2_a2/}
}
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Alexander D. Kolesnik. Cyclic planar random evolution with four directions. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2004), pp. 27-32. http://geodesic.mathdoc.fr/item/BASM_2004_2_a2/