This volume provides a unified mathematical introduction to stationary
time series models and to continuous time stationary stochastic
processes. The analysis of these stationary models is carried out in
time domain and in frequency domain. It begins with a practical
discussion on stationarity, by which practical methods for obtaining
stationary data are described. The presented topics are illustrated by
numerous examples. Readers will find the following covered in a
comprehensive manner:
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Autoregressive and moving average time series.
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Important properties such as causality.
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Autocovariance function and the spectral distribution of these models.
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Practical topics of time series like filtering and prediction.
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Basic concepts and definitions on the theory of stochastic processes,
such as Wiener measure and process.
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General types of stochastic processes such as Gaussian, selfsimilar,
compound and shot noise processes.
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Gaussian white noise, Langevin equation and Ornstein-Uhlenbeck
process.
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Important related themes such as mean square properties of stationary
processes and mean square integration.
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Spectral decomposition and spectral theorem of continuous time
stationary processes. This central concept is followed by the theory
of linear filters and their differential equations.
At the end, some selected topics such as stationary random fields,
simulation of Gaussian stationary processes, time series for planar
directions, large deviations approximations and results of information
theory are presented. A detailed appendix containing complementary
materials will assist the reader with many technical aspects of the
book.
