An Introduction to Probability Theory and Its Applications - William Feller

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Auteur(s) : William Feller - Feller

Editeur : John Wiley & Sons, Inc.

Langue : Anglais

Parution : 31/12/1990

Format : Moyen, de 350g à 1kg

Nombre de pages : 696

Nombre de livres : 1

Expédition : 1112

Dimensions : 22.9 x 15.2 x 4.1

ISBN : 0471257095

Résumé :

The classic text for understanding complex statistical probability

An Introduction to Probability Theory and Its Applications offers comprehensive explanations to complex statistical problems. Delving deep into densities and distributions while relating critical formulas, processes and approaches, this rigorous text provides a solid grounding in probability with practice problems throughout. Heavy on application without sacrificing theory, the discussion takes the time to explain difficult topics and how to use them. This new second edition includes new material related to the substitution of probabilistic arguments for combinatorial artifices as well as new sections on branching processes, Markov chains, and the DeMoivre-Laplace theorem.

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Biographie:

William Vilim Feller was a Croatian-American mathematician specializing in probability theory....

Sommaire:
Chapter I The Exponential and the Uniform Densities

1. Introduction

2. Densities. Convolutions

3. The Exponential Density

4. Waiting Time Paradoxes. The Poisson Process

5. The Persistence of Bad Luck

6. Waiting Times and Order Statistics

7. The Uniform Distribution

8. Random Splittings

9. Convolutions and Covering Theorems

10. Random Directions

11. The Use of Lebesgue Measure

12. Empirical Distributions

13. Problems for Solution

Chapter II Special Densities. Randomization

1. Notations and Conventions

2. Gamma Distributions

3. Related Distributions of Statistics

4. Some Common Densities

5. Randomization and Mixtures

6. Discrete Distributions

7. Bessel Functions and Random Walks

8. Distributions on a Circle

9. Problems for Solution

Chapter III Densities in Higher Dimensions. Normal Densities and Processes

1. Densities

2. Conditional Distributions

3. Return to the Exponential and the Uniform Distributions

4. A Characterization of the Normal Distribution

5. Matrix Notation. The Covariance Matrix

6. Normal Densities and Distributions

7. Stationary Normal Processes

8. Markovian Normal Densities

9. Problems for Solution

Chapter IV Probability Measures and Spaces

1. Baire Functions

2. Interval Functions and Integrals in R^r

3. ?-Algebras. Measurability

4. Probability Spaces. Random Variables

5. The Extension Theorem

6. Product Spaces. Sequences of Independent Variables

7. Null Sets. Completion

Chapter V Probability Distributions in R^r

1. Distributions and Expectations

2. Preliminaries

3. Densities

4. Convolutions

5. Symmetrization

6. Integration by Parts. Existence of Moments

7. Chebyshev?s Inequality

8. Further Inequalities. Convex Functions

9. Simple Conditional Distributions. Mixtures

10. Conditional Distributions

11. Conditional Expectations

12. Problems for Solution

Chapter VI A Survey of Some Important Distributions and Processes

1. Stable Distributions in R¹

2. Examples

3. Infinitely Divisible Distributions in R¹

4. Processes with Independent Increments

5. Ruin Problems in Compound Poisson Processes

6. Renewal Processes

7. Examples and Problems

8. Random Walks

9. The Queuing Process

10. Persistent and Transient Random Walks

11. General Markov Chains

12. Martingales

13. Problems for Solution

Chapter VII Laws of Large Numbers. Applications in Analysis

1. Main Lemma and Notations

2. Bernstein Polynomials. Absolutely Monotone Functions

3. Moment Problems

4. Application to Exchangeable Variables

5. Generalized Taylor Formula and Semi-Groups

6. Inversion Formulas for Laplace Transforms

7. Laws of Large Numbers for Identically Distributed Variables

8. Strong Laws

9. Generalization to Martingales

10. Problems for Solution

Chapter VIII The Basic Limit Theorems

1. Convergence of Measures

2. Special Properties

3. Distributions as Operators

4. The Central Limit Theorem

5. Infinite Convolutions

6. Selection Theorems

7. Ergodic Theorems for Markov Chains

8. Regular Variation

9. Asymptotic Properties of Regularly Varying Functions

10. Problems for Solution

Chapter IX Infinitely Divisible Distributions and Semi-Groups

1. Orientation

2. Convolution Semi-Groups

3. P...