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

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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. 
@article{BASM_2006_2_a6,
     author = {Alexander D. Kolesnik},
     title = {Discontinuous term of the distribution for {Markovian} random evolution in~$\mathrm R^3$},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {62--68},
     publisher = {mathdoc},
     number = {2},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2006_2_a6/}
}
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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/