Modeling of nonlinear colored noise in stable distribution environments

Stable processes can better model the impulsive random signals and noises in physical observations. This paper briefly introduces the statistical characteristics of a stable distribution, describes its spectral representation, proposes a new different spectral density from power spectrum density of second order processes, thus we can get a new concept of stable white noise based on a covariation sequence and covariation spectrum, which generalizes the conventional Gaussian white noise based on second order statistics. In addition, we propose a new technique for the estimation of the parameters of PAR (polynomial autoregressive) nonlinear colored noise processes with stable white noise innovations in PAR nonlinear systems.