The identification and estimation of nonlinear stochastic systems

This chapter describes what might be called the system, theorist's approach to understanding dynamics of nonlinear stochastic systems. The method uses so-called state-dependent parameters, and is able to handle non-stationarity, as long as the state-dependent parameters vary slowly compared to the significant dynamics. One of the main points made here is that most realistic systems have time-varying inputs which can be measured; models must take this into account, and indeed modeling often becomes easier rather than harder when this as done. We describe the methods used, based on recursive fixed-interval smoothing, and present applications to some realistic problems.