Author | Rosenblatt, M. author |
---|---|
Title | Random Processes [electronic resource] / by M. Rosenblatt |
Imprint | New York, NY : Springer New York, 1974 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-9852-6 |
Descript | 228 p. online resource |
I. Introduction -- II. Basic Notions for Finite and Denumerable State Models -- a. Events and Probabilities of Events -- b. Conditional Probability, Independence, and Random Variables -- c. The Binomial and Poisson Distributions -- d. Expectation and Variance of Random Variables (Moments) -- e. The Weak Law of Large Numbers and the Central Limit Theorem -- f. Entropy of an Experiment -- g. Problems -- III. Markov Chains -- a. The Markov Assumption -- b. Matrices with Non-negative Elements (Approach of Perron-Frobenius) -- c. Limit Properties for Markov Chains -- d. Functions of a Markov Chain -- e. Problems -- IV. Probability Spaces with an Infinite Number of Sample Points -- a. Discussion of Basic Concepts -- b. Distribution Functions and Their Transforms -- c. Derivatives of Measures and Conditional Probabilities -- d. Random Processes -- e. Problems -- V. Stationary Processes -- a. Definition -- b. The Ergodic Theorem and Stationary Processes -- c. Convergence of Conditional Probabilities -- d. MacMillanโs Theorem -- e. Problems -- VI. Markov Processes -- a. Definition -- b. Jump Processes with Continuous Time -- c. Diffusion Processes -- d. A Refined Model of Brownian Motion -- e. Pathological Jump Processes -- f. Problems -- VII. Weakly Stationary Processes and Random Harmonic Analysis -- a. Definition -- b. Harmonic Representation of a Stationary Process and Random Integrals -- c. The Linear Prediction Problem and Autoregressive Schemes -- d. Spectral Estimates for Normal Processes -- e. Problems -- VIII. Martingales -- a. Definition and Illustrations -- b. Optional Sampling and a Martingale Convergence Theorem -- c. A Central Limit Theorem for Martingale Differences -- d. Problems -- IX. Additional Topics -- a. A Zero-One Law -- b. Markov Chains and Independent Random Variables -- c. A Representation for a Class of Random Processes -- d. A Uniform Mixing Condition and Narrow Band-Pass Filtering -- e. Problems -- References