Well-posedness of the Fokker–Planck equation in a scattering process

The Fokker–Planck equation is usually used as an approximation of the linear transport equation for a highly forward peaked scattering process. In this note, we provide a rigorous proof for the solution existence and uniqueness of a boundary value problem to the Fokker–Planck equation. In addition, we present a result on the positivity of the solution.