A Planar Random Motion with an Infinite Number of Directions Controlled by the Damped Wave Equation

Abstract

We consider the planar random motion of a particle that moves with constant finite speed c and, at Poisson-distributed times, changes its direction θ with uniform law in [0, 2π). This model represents the natural two-dimensional counterpart of the wellknown Goldstein–Kac telegraph process. For the particle’s position (X(t), Y (t)), t > 0, we obtain the… (More)

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