Correlation Theory of Stationary and Related Random Functions

The theory of random functions is a very important and advanced part of modem probability theory, which is very interesting from the mathematical point of view and has many practical applications. In applications, one has to deal particularly often with the special case of stationary random functions. Such functions naturally arise when one considers a series of observations x(t) which depend on the real-valued or integer-valued ar­ gument t ("time") and do not undergo any systematic changes, but only fluctuate in a disordered manner about some constant mean level. Such a time series x(t) must naturally be described statistically, and in that case the stationary random function is the most appropriate statistical model. Stationary time series constantly occur in nearly all the areas of modem technology (in particular, in electrical and radio engineering, electronics, and automatic control) as well as in all the physical and geophysical sciences, in many other ap­ mechanics, economics, biology and medicine, and also plied fields. One of the important trends in the recent development of science and engineering is the ever-increasing role of the fluctuation phenomena associated with the stationary disordered time series. Moreover, at present, more general classes of random functions related to a class of stationary random functions have also been appearing quite often in various applied studies and hence have acquired great practical importance.