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Stationary Stochastic Processes for Scientists and Engineers

By Georg Lindgren, Holger Rootzen, Maria Sandsten

Chapman and Hall/CRC – 2013 – 330 pages

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  • Add to CartHardback: $79.95
    978-1-46-658618-5
    October 11th 2013

Description

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.

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.

Name: Stationary Stochastic Processes for Scientists and Engineers (Hardback)Chapman and Hall/CRC 
Description: By Georg Lindgren, Holger Rootzen, Maria Sandsten. 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...
Categories: Statistics & Probability, Probability, Statistical Theory & Methods