On the expansion of a bivariate distribution and its relationship to the output of a nolinearity

The series expansion of a bivariate distribution and the series expansion of the output of a nonlinearity are considered, as well as the relationship between these two problems. Three distinct expansions of bivariate distributions are presented along with a constructive procedure to obtain them explicitly. The cross-covarianee property and certain results on the expansion of the output of a nonlinearity are extended to a larger class of random processes.