Under very mild conditions, we prove that the number of components in a decomposable logarithmic combinatorial structure has a distribution which is close to Poisson in total variation. The conditions are satisfied for all assemblies, multisets and selections in the logarithmic class.The error in the Poisson approximation is shown under marginally more restrictive conditions to be of exact orde...

Abstract. The paper deals with the diffusion approximation of the Boltzmann equation for semiconductors in the presence of spatially oscillating electrostatic potential. When the oscillation period is of the same order of magnitude as the mean free path, the asymptotics leads to the Drift-Diffusion equation with a homogenized electrostatic potential and a diffusion matrix involving the small sc...

It might be that the two fundamental distributions in probability are the normal and the Poisson. Making these into processes with independent incre-Nevertheless, graduate training in probability tends to ignore Poisson processes and none of the almost 200 entries in the Probability and Statistics category of the 1991 Mathematics Subject Classification explicitly mentions Poisson, either. Brown...

(ABSTRACT) Random variables defined on the natural numbers may often be approximated by Poisson variables. Just as normal approximations may be improved by saddlepoint methods, Pois-son approximations may be substantially improved by tilting, expansion, and other related methods. This work will develop and examine the use of these methods, as well as present examples where such methods may be n...