Geodesic
Discontinuous term of the distribution for Markovian random evolution in $\mathrm R^3$
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2006), pp. 62-68 
Alexander D. Kolesnik. Discontinuous term of the distribution for Markovian random evolution in $\mathrm R^3$. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2006), pp. 62-68. http://geodesic.mathdoc.fr/item/BASM_2006_2_a6/
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     title = {Discontinuous term of the distribution for {Markovian} random evolution in~$\mathrm R^3$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the random motion at constant finite speed in the space $R^3$ 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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