Singularities in Quasidistributions, Their Regularization, and Nonclassical Number and Wave Statistics

Compared with earlier investigations we follow a way of arising singularities in quasidistributions as related to nonclassical photocount and wave statistics for nonlinear optical processes described by Gaussian statistics, also from the point of view of testing functions. Further we illustrate a process of regularization of singular quasidistributions so that regularized quasidistributions can provide measurable quantities. Results obtained can be applied to optical down-conversion as well as to Raman scattering provided that classical strong coherent pumping fields are used.