Stationary stochastic processes for scientists and engineers /
"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...
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton :
CRC Press, Taylor and Francis Group,
2014.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of 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.