TABLE OF CONTENTS We might think of a stochastic process as a physical phenomenon that involves two distinctive domains: the process domain and the observation domain. The process domain provides a model that describes in some way how the process will vary with time. For example, we may be able to fashion a time periodic function that describes the daily temperature at a certain geographical spot. Of course, this will not mean that the temperature at any time will be as prescribed by the model or even be closer to it; but this might provide a guideline to what the temperature will be. Therefore we strive to find a mathematical model that shows how the process varies with time.
The stochastic process will evolve with or without our knowledge (provided that we do not interfere with it), but we will be completely oblivious to it unless we have some means of observing the phenomenon. Continuing with our example, we will be able to know how the temperature varies only if we have a thermometer at this spot of interest. We might include a pressure and humidity sensors to see what kind of influence, if any, on the behavior of the temperature variation.
With the process domain, there are uncertainties that prevent the process from following the mathematical model. Likewise, no matter how accurate the thermometer is, there will be uncertainties about its measurements. Before we continue, we elaborate a bit on the concept of the state . The state of a stochastic...
