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Book Cover
E-book
Author Lindgren, Georg, 1940-

Title Stationary stochastic processes : theory and applications / Georg Lindgren
Published [Place of publication not identified] : Chapman and Hall/CRC, 2012
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Description 1 online resource : illustrations
Series Chapman & Hall/CRC texts in statistical science series
Contents <P><STRONG>Some Probability and Process Background<BR></STRONG>Sample space, sample function, and observables<BR>Random variables and stochastic processes<BR>Stationary processes and fields<BR>Gaussian processes<BR>Four historical landmarks<BR><B><BR></B><STRONG>Sample Function Properties</STRONG><B><BR></B>Quadratic mean properties<BR>Sample function continuity<BR>Derivatives, tangents, and other characteristics<BR>Stochastic integration<BR>An ergodic result<BR>Exercises<BR><B><BR></B><STRONG>Spectral Representations</STRONG><B><BR></B>Complex-valued stochastic processes<BR>Bochner's theorem and the spectral distribution<BR>Spectral representation of a stationary process<BR>Gaussian processes<BR>Stationary counting processes<BR>Exercises<BR><B><BR></B><STRONG>Linear Filters -- General Properties</STRONG><B><BR></B>Linear time invariant filters<BR>Linear filters and differential equations<BR>White noise in linear systems<BR>Long range dependence, non-integrable spectra, and unstable systems<BR>The ARMA-family<BR><BR><STRONG>Linear Filters -- Special Topics</STRONG><B><BR></B>The Hilbert transform and the envelope<BR>The sampling theorem<BR>Karhunen-Loève expansion<BR><B><BR></B><STRONG>Classical Ergodic Theory and Mixing</STRONG><B><BR></B>The basic ergodic theorem in <EM>L</EM>2<BR>Stationarity and transformations<BR>The ergodic theorem, transformation view<BR>The ergodic theorem, process view<BR>Ergodic Gaussian sequences and processes<BR>Mixing and asymptotic independence<BR><BR><STRONG>Vector Processes and Random Fields</STRONG><B><BR></B>Spectral representation for vector processes<BR>Some random field theory<BR>Exercises<BR><B><BR></B><STRONG>Level Crossings and Excursions</STRONG><B><BR></B>Level crossings and Rice's formula<BR>Poisson character of high-level crossings<BR>Marked crossings and biased sampling<BR>The Slepian model<BR>Crossing problems for vector processes and fields<BR><B><BR></B><STRONG>A Some Probability Theory</STRONG><B><BR></B>Events, probabilities, and random variables<BR>The axioms of probability<BR>Expectations<BR>Convergence<BR>Characteristic functions<BR>Hilbert space and random variables<BR><BR><STRONG>B Spectral Simulation of Random Processes</STRONG><B><BR></B>The Fast Fourier Transform, FFT<BR>Random phase and amplitude<BR>Simulation scheme<BR>Difficulties and details<BR>Summary<BR><B><BR></B><STRONG>C Commonly Used Spectra</STRONG><B><BR><BR></B><STRONG>D Solutions and Hints To Selected Exercises</STRONG><B><BR></B>Some probability and process background<BR>Sample function properties<BR>Spectral and other representations<BR>Linear filters -- general properties<BR>Linear filters -- special topics<BR>Ergodic theory and mixing<BR>Vector processes and random fields<BR>Level crossings and excursions<BR>Some probability theory<BR><B><BR></B><STRONG>Bibliography</STRONG><B><BR></B><STRONG>Index</P></STRONG>
Subject Stationary processes
Stochastic analysis
MATHEMATICS -- Probability & Statistics -- Bayesian Analysis.
MATHEMATICS -- Probability & Statistics -- General.
Stationary processes.
Stochastic analysis.
Form Electronic book
ISBN 146655780X
9781466557802