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Stationary Stochastic Processes : Theory and Applications

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Some Probability and Process BackgroundSample space, sample function, and observablesRandom variables and stochastic processesStationary processes and fieldsGaussian processesFour historical landmarksSample Function PropertiesQuadratic mean propertiesSample function continuityDerivatives, tangents, and other characteristicsStochastic integrationAn ergodic resultExercisesSpectral RepresentationsComplex-valued Read more...

Abstract: Some Probability and Process BackgroundSample space, sample function, and observablesRandom variables and stochastic processesStationary processes and fieldsGaussian processesFour historical landmarksSample Function PropertiesQuadratic mean propertiesSample function continuityDerivatives, tangents, and other characteristicsStochastic integrationAn ergodic resultExercisesSpectral RepresentationsComplex-valued stochastic processesBochner's theorem and the spectral distributionSpectral representation of a stationary processGaussian processesStationary counting processesExercisesLinear Filters - G

Author(s): Lindgren, Georg
Series: Chapman & Hall/CRC Texts in Statistical Science
Publisher: CRC Press
Year: 2012

Language: English
Pages: 367
City: Hoboken
Tags: Математика;Теория вероятностей и математическая статистика;Теория случайных процессов;

Content: Front Cover
Dedication
Contents
List of figures
Preface
Acknowledgments
List of notations
1. Some probability and process background
2. Sample function properties
3. Spectral representations
4. Linearfilters --
general properties
5. Linearfilters --
special topics
6. Classical ergodic theory and mixing
7. Vector processes and random fields
8. Level crossings and excursions
A. Some probability theory
B. Spectral simulation of random processes
C. Commonly used spectra
D. Solutions and hints to selected exercises
Bibliography