Kolmogorov equation solution: multiple scattering expansion and photon statistics evolution modeling

We consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering ampl itudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon number of finite and point receivers. Application to the LIDAR problem and X-ray beam scattering for orthogonal and inclined to a layer is considered.