On a completeness property of series expansions of bivariate densities

Random processes passed through zero memory nonlinearities are considered in terms of the preservation of mean square continuity. Then, series expansions of bivariate densities in orthonormal functions are treated, under the assumption that the bivariate density is associated with a first order stationary random process. It is shown that, if the random process is mean square continuous, then the orthonormal functions in the series expansion must be complete.