system model
Let $t=1,2,\mathrm{\dots}$ denote discrete time instants. By a system model we mean a mathematical model defined by a conditional probability^{} density function $f({y}_{t}{u}_{t},d(t1))$ where
 ${y}_{t}$

is the system output in time $t$,
 ${u}_{t}$

is the system input and
 $d(t1)$

denotes the sequence of data ${d}_{0},\mathrm{\dots},{d}_{t1}$ where ${d}_{t}=({u}_{t},{y}_{t})$.
Such a system has timeinvariant (constant) parameters. If the model parameters are unknown (uncertain, variable), we introduce the definition in the form $f({y}_{t}{u}_{t},d(t1),\theta )$. Here, $\theta $ is a (possibly multidimensional) parameter.
References
 1 Peterka, V., Bayesian Approach to System Identification, in Trends and Progress in System Identification, P. Ekhoff, Ed., pp. 239304. Pergamon Press, Oxford, 1981
Title  system model 

Canonical name  SystemModel 
Date of creation  20130322 18:33:34 
Last modified on  20130322 18:33:34 
Owner  camillio (22337) 
Last modified by  camillio (22337) 
Numerical id  6 
Author  camillio (22337) 
Entry type  Definition 
Classification  msc 93E03 