Geodesic
Random motion of particle in inhomogeneous 1D media with reflecting and absorbing barriers
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 1, pp. 81-91

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A random motion in 1D inhomogeneous media is considered. A moving particle changes abruptly a direction of velocity at Poisson times. The backward and forward Kolmogorov's equations describing this motion are derived. The explicit formulas for the probability distributions are obtained both for this motion and for the similar motions with reflecting and absorbing barriers. 
@article{TMF_1997_112_1_a3,
     author = {N. E. Ratanov},
     title = {Random motion of particle in inhomogeneous {1D} media with reflecting and absorbing barriers},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {81--91},
     publisher = {mathdoc},
     volume = {112},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a3/}
}
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N. E. Ratanov. Random motion of particle in inhomogeneous 1D media with reflecting and absorbing barriers. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 1, pp. 81-91. http://geodesic.mathdoc.fr/item/TMF_1997_112_1_a3/