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IMI/Publicaţii/BASM/Ediţii/BASM n.2 (51), 2006/

Discontinuous term of the distribution for Markovian random evolution in R3.

Authors: Kolesnik Alexander

Abstract

We consider the random motion at constant finite speed in the space R3 subject to the control of a homogeneous Poisson process and with uniform choice of directions on the unit 3-sphere. We obtain the explicit forms of the conditional characteristic function and conditional distribution when one change of direction occurs. We show that this conditional distribution represents a discontinuous term of the transition function of the motion.

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