Stationary Stochastic Processes for Scientists and Engineers
By Georg Lindgren, Holger Rootzen, Maria Sandsten
To Be Published August 1st 2013 by Chapman and Hall/CRC – 328 pages
Description
Based on a course taught to undergraduate students in engineering for over 30 years, this textbook presents all the material for a first course in stationary stochastic processes (SSP). Following naturally from a mathematical statistics course, it covers model building via SSP with a focus on engineering applications. The book includes many exercises and computer-based practicals using MATLAB®. A solutions manual and figure slides are available upon qualifying course adoption.
Reviews
This book is a lucid and well-paced introduction to stationary stochastic processes, superbly motivated and illustrated through a wealth of convincing applications in science and engineering. It offers a clear guide to the formulation and mathematical properties of these processes and to some non-stationary processes too, without going too deeply into the mathematical foundations; the emphasis throughout is on practical application rather than mathematical development for its own sake. The reader will find tools for analysis and calculation and also—importantly—material to deepen understanding and generate enthusiasm and confidence. An outstanding text.
—Clive Anderson, Department of Probability and Statistics, University of Sheffield
Contents
Stochastic Processes
Some stochastic models
Definition of a stochastic process
Distribution functions
Stationary Processes
Introduction
Moment functions
Stationary processes
Random phase and amplitude
Estimation of mean value and covariance function
Stationary processes and the non-stationary reality
Monte Carlo simulation from covariance function
The Poisson Process and Its Relatives
Introduction
The Poisson process
Stationary independent increments
The covariance intensity function
Spatial Poisson process
Inhomogeneous Poisson process
Monte Carlo simulation of Poisson processes
Spectral Representations
Introduction
Spectrum in continuous time
Spectrum in discrete time
Sampling and the aliasing effect
A few more remarks and difficulties
Monte Carlo simulation from spectrum
Gaussian Processes
Introduction
Gaussian processes
The Wiener process
Relatives of the Gaussian process
The Lévy process and shot noise process
Simulation of Gaussian process from spectrum
Linear Filters—General Theory
Introduction
Linear systems and linear filters
Continuity, differentiation, integration
White noise in continuous time
Cross-covariance and cross-spectrum
AR, MA, and ARMA Models
Introduction
Auto-regression and Moving average
Estimation of AR parameters
Prediction in AR and ARMA models
A simple non-linear model—the GARCH process
Monte Carlo simulation of ARMA processes
Linear Filters—Applications
Introduction
Differential equations with random input
The envelope
Matched filter
Wiener filter
Kalman filter
An example from structural dynamics
Monte Carlo simulation in continuous time
Frequency Analysis and Spectral Estimation
Introduction
The periodogram
The discrete Fourier transform and the FFT
Bias reduction—data windowing
Reduction of variance
Appendix A: Some Probability and Statistics
Appendix B: Delta Functions and Stieltjes Integrals
Appendix C: Kolmogorov’s Existence Theorem
Appendix D: Covariance/Spectral Density Pairs
Appendix E: A Historical Background
References
Index
Exercises appear at the end of each chapter.
Related Subjects
Name: Stationary Stochastic Processes for Scientists and Engineers (Hardback) – Chapman and Hall/CRC
Description: By Georg Lindgren, Holger Rootzen, Maria Sandsten. Based on a course taught to undergraduate students in engineering for over 30 years, this textbook presents all the material for a first course in stationary stochastic processes (SSP). Following naturally from a mathematical statistics course, it covers...
Categories: Statistics & Probability, Probability, Statistical Theory & Methods