Within the approach derived in the paper, the statistical linearization of nonlinear dynamic systems is treated as a search of optimal, in the sense of given criteria, linear transformations in the Hilbert space of random functions Z(t,s). A concrete choice of the type of the inner product in Z(t,s) leads to various variants of models within a unique representation of the linearized models, with the choosing of the inner product as the mixed moment leading to the ordinary statistical linearization based on the use of the correlation functions of the input and output processes of a system. Since the correlation functions are not the consistent measures of dependence between random processes, using these may give rise to unacceptable results. The paper proposes a choice of the inner product in Z(t,s) providing to derive the required characteristics of the models linearized, based on the disperssion relationships. The dispersion functions, i.e. the covariances of the conditional means, provide handling the nonlinear structure of a system and it's input and output processes, and hence deriving the adequate models linearized.