Physical Langevin model and the time-series model in systems far from equilibrium
Kuniharu Kishida · Physical Review A · 1982
To bridge the gap between a physical Langevin equation and a stochastic equation used in the time-series analysis, and to clarify the physical foundations of the latter, the time-series model from the Langevin equation is derived with the aid of two manipulations---elimination of irrelevant variables and projection of state variables upon a space spanned by observed quantities. The order of the two manipulations is shown to be important to find an equation called the Kalman filter in control theory. All the results are summarized in a concise schematic diagram which relates various models and equations established so far in different fields.