About two types of Nonstationary Stochastic Processes

Abstract

Based on satisfactory results of the early developed analytic approach application to analysis of 3-rd order non-stationary stochastic processes (NSPs), the well known mathematical procedure for describing a NSP in more detail was applied  to analysis of  the 2-nd order ones. Physical bases of the  2-nd order and  3-rd order NSPs  were defined as various periods of the NSP development. Based on numerous experimental data the periods were defined as: incubation (preliminary), intensive development, saturation for a 3-rd order NSP and period of intensive development together with the saturation  one for a 2-nd order NSP. The constitutive equation for the 2-nd order NSP was derived and analytically solved. Some basic properties of the solutions were considered. Full absence of an equilibrium specific point for a 2-nd order NSP and existence of oscillating trajectories in the phase spaces were shown. The combination of the revealed variants of a 2-nd order NSP development was explained by an action of the mechanism early proposed for the describing the 3-rd order NSPs development. The obtained results were interpreted in terms of unlimited number of 2-nd order NSPs development in  countless Universes similar to ourself.