Description
Stationary Stochastic Processes for Scientists and Engineers
Authors: Lindgren Georg, Rootzen Holger, Sandsten Maria
Language: EnglishSubject for Stationary Stochastic Processes for Scientists and Engineers:
Keywords
Sea Surface Height; Random Telegraph Signal; Stochastic processes in science and engineering; Covariance Function; understanding the mechanisms that generate stationary stochastic processes; Stationary Stochastic Processes; relationship between a covariance function and spectral density; Ornstein Uhlenbeck Process; difference between Fourier analysis of data and Fourier transformation of a covariance function; Spectral Density; AR; MA; ARMA; and GARCH models; Poisson Process; behavior of stochastic processes in linear filters; Inhomogeneous Poisson Process; Monte Carlo simulations of stochastic processes; 2π F0t; covariance and spectral estimation; Linear Filter; solution of linear stochastic differential equations; Coherence Spectrum; discrete-time auto-regressive and moving average processes; Ak Cos; Frequency Function; Wiener Process; Homogeneous Poisson Process; Gaussian Process; Uniform Conditional; Spatial Poisson Process; Yule Walker Equation; Spectrum Estimate; Stationary Gaussian Process; Hilbert Transform; Hanning Window; Efficient Monte Carlo Simulation; Cumulative Distribution Function
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Description
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Stochastic processes are indispensable tools for development and research in signal and image processing, automatic control, oceanography, structural reliability, environmetrics, climatology, econometrics, and many other areas of science and engineering. Suitable for a one-semester course, Stationary Stochastic Processes for Scientists and Engineers teaches students how to use these processes efficiently. Carefully balancing mathematical rigor and ease of exposition, the book provides students with a sufficient understanding of the theory and a practical appreciation of how it is used in real-life situations. Special emphasis is on the interpretation of various statistical models and concepts as well as the types of questions statistical analysis can answer.
The text first introduces numerous examples from signal processing, economics, and general natural sciences and technology. It then covers the estimation of mean value and covariance functions, properties of stationary Poisson processes, Fourier analysis of the covariance function (spectral analysis), and the Gaussian distribution. The book also focuses on input-output relations in linear filters, describes discrete-time auto-regressive and moving average processes, and explains how to solve linear stochastic differential equations. It concludes with frequency analysis and estimation of spectral densities.
With a focus on model building and interpreting the statistical concepts, this classroom-tested book conveys a broad understanding of the mechanisms that generate stationary stochastic processes. By combining theory and applications, the text gives students a well-rounded introduction to these processes. To enable hands-on practice, MATLAB® code is available online.
Stochastic Processes. Stationary Processes. The Poisson Process and Its Relatives. Spectral Representations. Gaussian Processes. Linear Filters—General Theory. AR, MA, and ARMA Models. Linear Filters—Applications. Frequency Analysis and Spectral Estimation. Appendices. References. Index.
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