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Stationary Random Functions (Processes)

  • V. A. Svetlitsky
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)

Abstract

Random processes that proceed in time with approximate homogeneity and have the form of continuous random oscillations about a certain mean value are widespread. Their probability characteristics do not depend on the choice of time reference point, i.e. are invariant relative to the shift of time. Accordingly, a random function X(t) is defined as stationary, if the probability characteristics of a random function X (t + t’) at any t’ coincide with the appropriate characteristics of X(t). This occurs only when the mathematical expectation and the variance of a random function do not depend on time, and the correlation function depends only on the difference of arguments (t’ − t). The stationary process may be considered as a process, that proceeds in time without limit In this context the stationary process is similar to the steady-state vibrations, whose parameters are independent of a time reference point.

Keywords

Correlation Function Spectral Density Stationary Function Random Function Linear Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • V. A. Svetlitsky
    • 1
  1. 1.The Department of Applied MechanicsBauman Moscow State Technical UniversityMoscowRussia

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