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. MacMillan's 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 aClass of Random Processes. - d. A Uniform Mixing Condition and Narrow Band-Pass Filtering. - e. Problems. - References. Language: English