Stationary Stochastic Processes for Scientists and Engineers

Name: Stationary Stochastic Processes for Scientists and Engineers
Availability: InStock
ISBN: 9781466586185

ISBN-10: 1466586184

ISBN-13: 9781466586185

Edition: 2013

Authors: Georg Lindgren, Holger Lennart Rootzen, Maria Sandsten

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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.

Book details

Copyright year: 2013
Publisher: CRC Press LLC
Publication date: 10/11/2013
Binding: Hardcover
Pages: 330
Size: 6.50" wide x 9.25" long x 0.75" tall
Weight: 1.342
Language: English



Preface


A survey of the contents



Stochastic processes



Some stochastic models



Definition of a stochastic process



Distribution functions



The CDF family



Gaussian processes



Stationary processes



Introduction



Moment functions



The moment functions



Simple properties and rules



Interpretation of moments and moment functions



Stationary processes



Strictly stationary processes



Weakly stationary processes



Important properties of the covariance function



Random phase and amplitude



A random harmonic oscillation



Superposition of random harmonic oscillations



Power and average power



Estimation of mean value and covariance function



Estimation of the mean value function



Ergodicity



Estimating the covariance function



Ergodicity a second time



Processes with continuous time



Stationary processes and the non-stationary reality



Monte Carlo simulation from covariance function



Why simulate a stochastic process?



Simulation of Gaussian process from covariance function


Exercises



The Poisson process and its relatives



Introduction



The Poisson process



Definition and simple properties



Interarrival time properties



Some distribution properties



Stationary independent increments



A general class with interesting properties



Covariance properties



The covariance intensity function



Correlation intensity



Counting processes with correlated increments



Spatial Poisson process



Inhomogeneous Poisson process



Monte Carlo simulation of Poisson processes



Homogeneous Poisson processes in R and R<sup>n<sup>



Inhomogeneous Poisson processes


Exercises



Spectral representations



Introduction



Spectrum in continuous time



Definition and general properties



Continuous spectrum



Some examples



Discrete spectrum



Spectrum in discrete time



Definition



Fourier transformation of data



Sampling and the aliasing effect



A few more remarks and difficulties



The sampling theorem



Fourier inversion



Spectral representation of the second-moment function b(ï¿½)



Beyond spectrum and covariance function



Monte Carlo simulation from spectrum


Exercises



Gaussian processes



Introduction



Gaussian processes



Stationary Gaussian processes



Gaussian process with discrete spectrum



The Wiener process



The one-dimensional Wiener process



Self similarity



Brownian motion



Relatives of the Gaussian process



The Lï¿½vy process and shot noise process



The Lï¿½vy process



Shot noise



Monte Carlo simulation of a Gaussian process from spectrum



Simulation by random cosines



Simulation via covariance function


Exercises



Linear filters - general theory



Introduction



Linear systems and linear filters



Filter with random input



Impulse response



Moment relations



Frequency function and spectral relations



Continuity, differentiation, integration



Quadratic mean convergence in stochastic processes



Differentiation



Integration



White noise in continuous time



Cross-covariance and cross-spectrum



Definitions and general properties



Input-output relations



Interpretation of the cross-spectral density


Exercises



AR-, MA-, and ARMA-models



Introduction



Auto-regression and moving average



Auto-regressive process, AR(p)



Moving average, MA(q)



Mixed model, ARMA(p,q)



Estimation of AR-parameters



Prediction in AR- and ARMA-models



Prediction of AR-processes



Prediction of ARMA-processes



The covariance function for an ARMA-process



The orthogonality principle



A simple non-linear model - the GARCH-process



Monte Carlo simulation of ARMA processes


Exercises



Linear filters - applications



Introduction



Differential equations with random input



Linear differential equations with random input



Differential equations driven by white noise



The envelope



The Hilbert transform



A complex representation



The envelope of a narrow-banded process



Matched filter



Digital communication



A statistical decision problem



The optimal matched filter



Wiener filter



Reconstruction of a stochastic process



Optimal cleaning filter; frequency formulation



General solution; discrete time formulation



Kalman filter



The process and measurement models



Updating a conditional normal distribution



The Kalman filter



An example from structural dynamics



A one-wheeled car



A stochastic road model



Optimization



Monte Carlo simulation in continuous time


Exercises



Frequency analysis and spectral estimation



Introduction



The periodogram



Definition



Expected value



"Pre-whitening"



Variance



The discrete Fourier transform and the FFT



Bias reduction - data windowing



Reduction of variance



Lag windowing



Averaging of spectra



Multiple windows



Estimation of cross- and coherence spectrum


Exercises



Some probability and statistics


A.1



Multidimensional normal distribution



Conditional normal distribution



Complex normal variables



Convergence in quadratic mean



Some statistical theory



Delta functions, generalized functions, and Stieltjes integrals



Introduction



The delta function



Formal rules for density functions



Distibutions of mixed type



Generalized functions



Stieltjes integrals



Definition



Some simple properties



Kolmogorov's existence theorem



The probability axioms



Random variables



Stochastic processes



Covariance/spectral density pairs



A historical background


References


Index