An Introduction to Measure-Theoretic Probability, Second Edition, employs a classical approach to teaching students of statistics, mathematics, engineering, econometrics, finance, and other disciplines measure-theoretic probability. This book requires no prior knowledge of measure theory, discusses all its topics in great detail, and includes one chapter on the basics of ergodic theory and one chapter on two cases of statistical estimation. There is a considerable bend toward the way probability is actually used in statistical research, finance, and other academic and nonacademic applied pursuits. Provides in a concise, yet detailed way, the bulk of probabilistic tools essential to a student working toward an advanced degree in statistics, probability, and other related fieldsIncludes extensive exercises and practical examples to make complex ideas of advanced probability accessible to graduate students in statistics, probability, and related fieldsAll proofs presented in full detail and complete and detailed solutions to all exercises are available to the instructors on book companion site INDICE: Preface1. Certain Classes of Sets, Measurability, Pointwise Approximation2. Definition and Construction of a Measure and Its Basic Properties3. Some Modes of Convergence of a Sequence of Random Variables and Their Relationships4. The Integral of a Random Variable and Its Basic Properties5. Standard Convergence Theorems, The Fubini Theorem6. Standard Moment and Probability Inequalities, Convergence in the r-th Mean and Its Implications7. The Hahn-Jordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and The Radon-Nikcodym Theorem8. Distribution Functions and Their Basic Properties, Helly-Bray Type Results9. Conditional Expectation and Conditional Probability, and Related Properties and Results10. Independence11. Topics from the Theory of Characteristic Functions12. The Central Limit Problem: The Centered Case13. The Central Limit Problem: The Noncentered Case14. Topics from Sequences of Independent Random Variables15. Topics from Ergodic Theory
- ISBN: 978-0-12-800042-7
- Editorial: Academic Press
- Encuadernacion: Cartoné
- Páginas: 464
- Fecha Publicación: 13/05/2014
- Nº Volúmenes: 1
- Idioma: Inglés