Graduate Texts in Mathematics ProbabilityPDF电子书下载
外文
- 作 者：
- 出 版 社：
- 出版年份：2222
- ISBN：0387908986
- 页数：577 页
图书介绍： 查看图书目录点击购买PDF全本电子书 上一篇：INTRODUCTION TO FINANCIAL ACCOUNTING下一篇：NUMERICAL METHODS AND SOFTWARE 《Graduate Texts in Mathematics Probability》目录 标签：
Introduction1
CHAPTER Ⅰ Elementary Probability Theory5
1.Probabilistic Model of an Experiment with a Finite Number of Outcomes5
2.Some Classical Models and Distributions17
3.Conditional Probability.Independence23
4.Random Variables and Their Properties32
5.The Bernoulli Scheme.Ⅰ.The Law of Large Numbers45
6.The Bernoulli Scheme.Ⅱ.Limit Theorems （Local,De Moivre-Laplace, Poisson）55
7.Estimating the Probability of Success in the Bernoulli Scheme68
8.Conditional Probabilities and Mathematical Expectations withRespect to Decompositions74
9.Random Walk.I.Probabilities of Ruin and Mean Duration inCoin Tossing81
10.Random Walk.Ⅱ.Reflection Principle.Arcsine Law92
11.Martingales.Some Applications to the Random Walk101
12.Markov Chains.Ergodic Theorem.Strong Markov Property108
CHAPTER Ⅱ Mathematical Foundations of Probability Theory129
1.Probabilistic Model for an Experiment with Infinitely ManyOutcomes.Kolmogorov’s Axioms129
2.Algebras and σ-algebras.Measurable Spaces137
3.Methods of Introducing Probability Measures on Measurable Spaces149
4.Random Variables.Ⅰ164
5.Random Elements174
6.Lebesgue Integral Expectation178
7.Conditional Probabilities and Conditional Expectations with Respect to a σ-Algebra210
8.Random Variables.Ⅱ232
9.Construction of a Process with Given Finite-Dimensional Distribution243
10.Various Kinds of Convergence of Sequences of Random Variables250
11.The Hilbert Space of Random Variables with Finite Second Moment260
12.Characteristic Functions272
13.Gaussian Systems295
CHAPTER Ⅲ Convergence of Probability Measures.Central Limit Theorem306
1.Weak Convergence of Probability Measures and Distributions306
2.Relative Compactness and Tightness of Families of Probability Distributions314
3.Proofs of Limit Theorems by the Method of Characteristic Functions318
4.Central Limit Theorem for Sums of Independent Random Variables326
5.Infinitely Divisible and Stable Distributions335
6.Rapidity of Convergence in the Central Limit Theorem342
7.Rapidity of Convergence in Poisson’s Theorem345
CHAPTER Ⅳ Sequences and Sums of Independent Random Variables354
1.Zero-or-One Laws354
2.Convergence of Series359
3.Strong Law of Large Numbers363
4.Law of the Iterated Logarithm370
CHAPTER Ⅴ Stationary （Strict Sense） Random Sequences and Ergodic Theory376
1.Stationary （Strict Sense） Random Sequences.Measure-Preserving Transformations376
2.Ergodicity and Mixing379
3.Ergodic Theorems381
CHAPTER Ⅵ Stationary （Wide Sense） Random Sequences.L2 Theory387
1.Spectral Representation of the Covariance Function387
2.Orthogonal Stochastic Measures and Stochastic Integrals395
3.Spectral Representation of Stationary （Wide Sense） Sequences401
4.Statistical Estimation of the Covariance Function and the Spectral Density412
5.Wold’s Expansion418
6.Extrapolation, Interpolation and Filtering425
7.The Kalman-Bucy Filter and Its Generalizations436
CHAPTER Ⅶ Sequences of Random Variables that Form Martingales446
1.Definitions of Martingales and Related Concepts446
2.Preservation of the Martingale Property Under Time Change at a Random Time456
3.Fundamental Inequalities464
4.General Theorems on the Convergence of Submartingales and Martingales476
5.Sets of Convergence of Submartingales and Martingales483
6.Absolute Continuity and Singularity of Probability Distributions492
7.Asymptotics of the Probability of the Outcome of a Random Walk with Curvilinear Boundary504
8.Central Limit Theorem for Sums of Dependent Random Variables509
CHAPTER Ⅷ Sequences of Random Variables that Form Markov Chains523
1.Definitions and Basic Properties523
2.Classification of the States of a Markov Chain in Terms of Arithmetic Properties of the Transition Probabilities p（n）ij528
3.Classification of the States of a Markov Chain in Terms of Asymptotic Properties of the Probabilities p（n）ij532
4.On the Existence of Limits and of Stationary Distributions541
5.Examples546
Historical and Bibliographical Notes555
References561
Index of Symbols565
Index569
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摘要：本文详细介绍了《Graduate Texts in Mathematics Probability.pdf》电子书版文档的下载，从书籍内容、下载途径、适用人群和学术价值四个方面进行了全面阐述，旨在为读者提供一份全面、实用的参考。
1、书籍内容
《Graduate Texts in Mathematics Probability.pdf》是一本关于概率论的学术著作，涵盖了概率论的基本概念、理论和方法。书中详细介绍了概率论的基本原理，包括随机事件、概率分布、随机变量、大数定律和中心极限定理等。此外，书中还涉及了概率论在统计学、金融学、物理学等领域的应用。
本书内容丰富，结构严谨，适合作为高等学府研究生和科研人员的参考书籍。书中不仅对概率论的基本理论进行了深入探讨，还结合实际应用，使读者能够更好地理解和掌握概率论的知识。
此外，本书还包含大量的例题和习题，有助于读者巩固所学知识，提高解题能力。
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3、适用人群
《Graduate Texts in Mathematics Probability.pdf》主要面向高等学府的研究生和科研人员，尤其适合数学、统计学、物理学、金融学等相关专业的学生和研究人员。此外，对概率论感兴趣的读者也可以通过阅读本书，深入了解概率论的理论和应用。
本书内容深入浅出，既适合初学者入门，也适合有一定基础的学习者进一步深造。对于想要提高概率论知识水平、拓展学术视野的读者来说，本书是一本不可多得的佳作。
4、学术价值
《Graduate Texts in Mathematics Probability.pdf》作为一本概率论领域的经典著作，具有较高的学术价值。首先，本书系统地介绍了概率论的基本理论和方法，为读者提供了全面、系统的概率论知识体系。
其次，本书在概率论的应用方面具有很高的参考价值，有助于读者将概率论知识应用于实际问题。此外，本书的作者在概率论领域具有较高的学术地位，其研究成果和观点对概率论的发展具有重要意义。
总之，《Graduate Texts in Mathematics Probability.pdf》在概率论领域具有较高的学术价值，对于推动概率论的发展和应用具有重要意义。
总结：
本文从书籍内容、下载途径、适用人群和学术价值四个方面对《Graduate Texts in Mathematics Probability.pdf》电子书版文档进行了详细阐述。本书作为概率论领域的经典著作，具有很高的学术价值和实用价值，适合广大读者阅读和学习。
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