概率論

內(nèi)容概要

In the Preface to the first edition, originally published in 1980, we mentioned that this book was based on the author's lectures in the Department of Mechanics and Mathematics of the Lomonosov University in Moscow, which were issued, in part, in mimeographed form under the title "Probability, Statistics, and Stochastic Processors, I, II" and published by that University. Our original intention in writing the first edition of this book was to divide the contents into three parts: probability, mathematical statistics, and theory of stochastic processes, which corresponds to an outline of a threesemester course of lectures for university students of mathematics. However, in the course of preparing the book, it turned out to be impossible to realize this intention completely, since a full exposition would have required too much space. In this connection, we stated in the Preface to the first edition that only probability theory and the theory of random processes with discrete time were really adequately presented.

作者簡(jiǎn)介

作者:( )A.N.Shiryaev[

書(shū)籍目錄

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 TheoremCHAPTER IV  Sequences and Sums of Independent Random VariablesCHAPTER V Stationary(Stircty Sense)Random Sequences and Ergodic TheoryCHAPTER VI Stationary(Wide Sense)Random Sequences L2 TheoryCHAPTER VII Sequences of Random Variables that Form MartingalseCHAPTER VIII Sequences of Random Variables that Form Markov ChainsHistorical and Bibographical NotesReferncesIndex of SymbolsIndex

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