In this chapter we introduce basic concepts necessary to study the timedependent dynamics of random phenomena. The latter will be modeled as a family of random quantities indexed by a parameter, interpreted in this book as time. The parameter may be either continuous or discrete. Depending on the context and the tradition followed by different authors, such families are called random signals, stochastic processes, or random time series. The emphasis here is on random dynamics which are stationary, that is governed by underlying statistical mechanisms that do not change in time, although, of course, particular realizations of such families will be functions that vary with time. Think here about the random signal produced by the proverbial repeated coin tossing; the outomes vary while the fundamental mechanics remains the same.


White Noise Autocorrelation Function Sleep Stage Random Quantity Random Signal 
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  1. 27.
    See, for example, O. Kallenberg, Foundations of Modern Probability, Springer-Verlag, New York, 1997.MATHGoogle Scholar
  2. 29.
    For a thorough exposition of these issues, see, for example, P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, Springer-Verlag, New York, 1991.Google Scholar

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