The concept of a stochastic process is complex. A simple presentation of the fundamental ideas is given here. Our prime purposes are to define notation and to motivate the reader to review a detailed text. However, note at this stage that noise models in terms of stochastic processes can be used in various ways. One possibility is to let the noise models describe random disturbances that are assumed to be present. Sensor noise and the effects of unmodeled sources in dynamic systems are typical interpretations of such descriptions. Another possibility is to use the noise model as a means of expressing model uncertainties. If the model description relating input and output variables of a dynamic system is uncertain, such uncertainties may be incorporated in a noiseNoiseprocess model. Some ideas along this line will be presented in the next chapter. A third possibility is to regard the noise as a tuning variable when constructing a filter. By changing the noise model parameters, a user can change the frequency properties of an associated optimal filter. The idea will be illustrated in chaps. 7 and 8 . Finally, a noise model can be used as means of achieving certain good properties of a feedback system designed by stochastic control theory. The last idea will not be discussed in this book, because the book is devoted to modeling and analysis of stochastic signals and systems, but not to the control of a such system.