Diffusion Approximation of Transport Processes with General Reflecting Boundary Conditions

Diffusion approximations are obtained for time-homogeneous linear transport models with reflecting boundary conditions. The collision kernel is not required to satisfy any balance condition and the scattering kernel on the boundary is general enough to include all examples of boundary conditions known to the authors (with conservation of the number of particles) and, in addition, to model the Debye sheath. The mathematical approach does not rely on Hilbert expansions, but rather on martingale and stochastic averaging techniques.