Stochastic Identification Methods for Nonlinear Systems: An Extension of the Wiener Theory

The Wiener series provides a representation for many nonlinear systems with respect to Brownian motion inputs. In this paper the Wiener theory is extended to a wide class of stochastic inputs including Brownian motion (and white-noise). In particular, difficulties intrinsic to cross-correlation methods (like the Lee–Schetzen method) are discussed for several discrete-time random input processes used in biological applications.