State Space Models

Abstract

In Chapter 1 we argued that mathematical models obtained from first principles usually contain latent variables. Up to now these latent variables did not enter the mathematical development. In Chapters 5 and 6 latent variable systems will be pursued in full generality. In the present chapter we discuss a special and important class of latent variables, namely state variables. State variables either show up naturally in the modeling process or they can be artificially introduced. State variables have the property that they parametrize the memory of the system, i.e., that they “split” the past and future of the behavior. The precise meaning of this statement will be made clear in the sequel.