概率論

內容概要

This book is a complete revision of the earlier work Probability which appeared in 1970. While revised so radically and incorporating so much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim was stated as the provision of a 'first text in probability, demanding a reasonable but not extensive knowledge of mathematics, and taking the reader to what one might describe as a good intermediate level'. In doing so it attempted to break away from stereotyped applications, and consider applications of a more novel and significant character. The particular novelty of the approach was that expectation was taken as the prime concept, and the concept of expectation axiomatized rather than that of a probability measure. In the preface to the original text of 1970 (reproduced below, together with that to the Russian edition of 1982) I listed what I saw as the advantages of the approach in as unlaboured a fashion as I could. I also took the view that the text rather than the author should persuade, and left the text to speak for itself. It has, indeed, stimulated a steady interest, to the point that Springer-Verlag has now commissioned this complete reworking.

書籍目錄

Preface to the Third Edition Preface to Probability (1970) Preface to the Russian Edition of Probability (1982) CHAPTER1  Uncertainty， Intuition and Expectation   1.Ideas and Examples   2.The Empirical Basis   3.Averages over a Finite Population   4.Repeated Sampling: Expectation   5.More on Sample Spaces and Variables   6.Ideal and Actual Experiments: Observables CHAPTER2  Expectation   1.Random Variables   2.Axioms for the Expectation Operator   3.Events: Probability   4.Some Examples of an Expectation   5.Moments   6.Applications: Optimization Problems   7.Equiprobable Outcomes: Sample Surveys     8.Applications:Least Square Estimation of Random Variables  9.Some Implications of the AxiomxCHAPTER3  Probablility  1.Events,Sets and Indicatiors  2.Probability Measure  3.Expectation as a Probability Integral  4.Some History  5.Subjective ProbabilityCHAPTER4  Some Basic Models  1.A Model of Spatial Distribution  2.The Multinomial,Binomial,Poisson and Geometric Distributions  3.Independence  4.Probability Generating Functions  5.The St.Petersburg Paradox  6.Matching,and Other Combinatorial Problems  7.Conditioning  8.Variables on the Continuum:the Exponential and Gamma DistributionsCHAPTER5  Conditioning  1.Conditional Expectation  2.Conditional Probability  3.A Conditional Expectationas a Random Variable  4.Conditioning on a Field  5.Independence  6.Statistical decision Theory  7.Information Transmission  8.Acceptance SamplingCHAPTER6  Applications of the Independence Concept  1.Renewal Processes  2.Recurrent Events:Regeneration Points  3.A Result in Statistical Mechanics:the Gibbs Distribution  4.Branching ProcessesCHAPTER7  The Two Basic Limit Theorems  1.Convergence in Distribution(Weak Convergence)  2.Properties of the Characteristic Function  3.The Law of Large Numbers  4.Normal Convergence(the Central Limit Theorem)  5.The Normal DistributionCHAPTER8  Continuous Random Variables and Their Transformations  1.Distributions with a Density  2.Functions of Random Variables  3.Conditional DensitiesCHAPTER9  Markov Processes in Discrete Time  1.Stochastic Processes and the Markov Property  ……CHAPTER10  Markov Processes in Continuous TimeCHAPTER11  Second-Order TheoryCHAPTER12  Consistency and Extension:the Finite-Dimensional CaseCHAPTER13  Stochastic ConvergenceCHAPTER14  MartingalesCHAPTER15  Extension:Examples of the Infinite-Dimensional CaseCHAPTER16  Some Interesting ProcessesReferencesIndex

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