| Preface to the Second Edition Preface to the First Edition Introduction CHAPTER I Elementary Probability Theory 1. Probabilistic Model of an Experiment with a Finite Number of Outcomes 2. Some Classical Models and Distributions 3. Conditional Probability. Independence 4. Random Variables and Their Properties 5. The Bernoulli Scheme. I. The Law of Large Numbers 6. The Bernoulli Scheme. II. Limit Theorems (Local， De Moivre-Laplace， Poisson) 7. Estimating the Probability of Success in the Bernoulli Scheme 8. Conditional Probabilities and Mathematical Expectations with Respect to Decompositions 9. Random Walk. I. Probabilities of Ruin and Mean Duration in Coin Tossing 10. Random Walk. II. Reflection Principle. Arcsine Law 11. Martingales. Some Applications to the Random Walk 12. Markov Chains. Ergodic Theorem. Strong Markov Property CHAPTER II Mathematical Foundations of Probability Theory 1. Probabilistic Model for an Experiment with Infinitely Many Outcomes. Kolmogorov‘s Axioms 2. Algebras and a-algebras. Measurable Spaces 3. Methods of Introducing Probability Measures on Measurable Spaces …… CHAPTER III Conergence of Probability Measures.Central Limit Theorem CHAPTER IV Sequences and Sums of Independent Random Variables CHAPTER V Stationary(Stircty Sense)Random Sequences and Ergodic Theory CHAPTER VI Stationary(Wide Sense)Random Sequences L2 Theory CHAPTER VII Sequences of Random Variables that Form Martingalse CHAPTER VIII Sequences of Random Variables that Form Markov Chains Historical and Bibographical Notes Refernces Index of Symbols Index |
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