Rarefaction of moving diffusion particles - Gasanenko, V. A.; Roitman, A. B. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
We investigate a flow of particles moving along a tube together with gas. The dynamics of particles is determined by a stochastic differential equation with different initial states. The walls of the tube absorb particles. We prove that if the incoming flow of particles is determined by a random Poisson measure, then the number of remained particles is characterized by the Poisson distribution. The parameter of this distribution is constructed by using a solution of the corresponding parabolic boundary-value problem.