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: Autoregressive and moving average time series. Important properties such as causality. Autocovariance function and the spectral distribution of these models. Practical topics of time series like filtering and prediction. Basic concepts and definitions on the theory of stochastic processes, such as Wiener measure and process. General types of stochastic processes such as Gaussian, selfsimilar, compound and shot noise processes. Gaussian white noise, Langevin equation and Ornstein–Uhlenbeck process. Important related themes such as mean square properties of stationary processes and mean square integration. 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 and results of information theory are presented. A detailed appendix containing complementary materials will assist the reader with many technical aspects of the book.Key FeaturesThe topics are presented progressively, by going from discrete to continuous time, by studying connected questions and by completing abstract theory with compelling examplesSuited for upper-level undergraduate and graduate students, researchers in academia and scientists in industryCovers both fundamentals and practical aspects of stationary modelsThis book provides a unified presentation of stationary time series and continuous time stationary processesThe appendix provides complementary material that assists the reader with technical aspects of the book

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