Probability, random variables, and stochastic processes.
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| Format: | Book |
| Language: | English |
| Published: |
New York,
McGraw-Hill
[©1965]
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| Series: | McGraw-Hill series in systems science.
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| Subjects: |
Table of Contents:
- Probability and random variables. The meaning of probability: Preliminary remarks ; The various definitions of probability ; Determinism versus probability
- The axioms of probability: Set theory ; Probability space ; Conditional probabilities and independent events ; Summary
- Repeated trials: Combined experiments ; Bernoulli trials ; Asymptotic theorems ; Generalized Bernoulli trials ; Bayes' theorem in statistics
- The concept of a random variable: Random variables, distributions, densities ; Examples of distribution and density functions ; Conditional distributions and densities ; Bayes' theorem in statistics (reexamined)
- Functions of one random variable: The concept of a function of one random variable ; Determination of the distribution and density of y = g(x) ; Applications ; Expected value, dispersion, moments ; Characteristic functions
- Two random variables: Joint distribution and density functions ; Conditional distributions and densities ; Independent random variables ; Jointly normal random variables
- Functions of two random variables: One function of two random variables ; Two functions of two random variables ; Expected value, moments, characteristic functions ; Mean-square estimation, the orthogonality principle ; More on normal random variables
- Sequences of random variables: General concepts ; Mean, mean-square estimation, moments, characteristic functions ; Applications ; Normal random variables ; Convergence concepts and the law of large numbers ; The central-limit theorem.
- Stochastic processes. General concepts: Introduction remarks ; Special processes ; Definitions ; Stationary processes ; Transformation of stochastic processes (systems) ; Stochastic continuity and differentiation ; Stochastic differential equations ; Stochastic integrals, time averages, ergodicity
- Correlation and power spectrum of stationary processes: Correlation ; Power spectrum ; Linear systems ; Hilbert transforms, shot noise, thermal noise ; Mean-square periodicity and Fourier series ; Band-limited processes ; An estimate of the variation of a band-limited process
- Linear mean-square estimation: Introductory remarks ; The orthogonality principle in linear mean-square estimation ; The Wiener-Kolmogoroff theory ; The filtering problem ; The prediction problem ; Wide-sense Markoff sequences and recursive filtering
- Nonstationary processes; transients in linear systems with stochastic inputs: Transients in linear systems with stochastic inputs ; Two-dimensional Fourier transforms ; Time averages
- Harmonic analysis of stochastic processes: Series expansions ; Approximate Fourier expansion with uncorrelated coefficients ; Fourier transforms of stochastic processes ; Generalized harmonic analysis
- Stationary and nonstationary normal processes: General remarks ; Stationary processes ; Detection ; The zero-crossing problem ; Conditional densities and mean-square estimation ; Bandpass processes ; The Wiener-Levy process
- Brownian movement and Markoff processes: Langevin's equation ; Motion of a harmonically bound particle ; Markoff sequences ; Markoff processes
- Poisson process and shot noise: Poisson distributions ; Random points in time ; Shot noise ; Densities and characteristic functions ; High-density shot noise ; Square-law detection of shot noise.