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Stochastic convergence /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1975.
|
| Edición: | 2d ed. |
| Colección: | Probability and mathematical statistics ;
v. 30. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Stochastic Convergence; Copyright Page; Table of Contents; Preface to the Second Edition; Preface to the First Edition; List of Examples; Chapter 1. INTRODUCTION; 1.1. Survey of basic concepts; 1.2. Certain inequalities; 1.3. Characteristic functions; 1.4. Independence; 1.5. Monotone classes of sets (events); Exercises; Chapter 2. STOCHASTIC CONVERGENCE CONCEPTS AND THEIR PROPERTIES; 2.1. Definitions; 2.2. Relations among the various convergence concepts; 2.3. Convergence of sequences of mean values and of certain functions of random variables
- 2.4. Criteria for stochastic convergence2.5. Further modes of stochastic convergence; 2.6. Information convergence; Exercises; Chapter 3. SPACES OF RANDOM VARIABLES; 3.1. Convergence in probability; 3.2. Almost certain convergence; 3.3. The spaces Lp; 3.4. The space of distribution functions; Exercises; Chapter 4. INFINITE SERIES OF RANDOM VARIABLES AND RELATED TOPICS; 4.1. The lemmas of Borel-Cantelli and the zero-one laws; 4.2. Convergence of series; 4.3. Some limit theorems; Exercises; Chapter 5. RANDOM POWER SERIES; 5.1. Definition and convergence of random power series
- 5.2. The radius of convergence of a random power series5.3. Random power series with identically distributed coefficients; 5.4. Random power series with independent coefficients; 5.5. The analytic continuation of random power series; 5.6. Random entire functions; Exercises; Chapter 6. STOCHASTIC INTEGRALS AND DERIVATIVES; 6.1. Some definitions concerning stochastic processes; 6.2. Definition and existence of stochastic integrals; 6.3. L2-continuity and differentiation of stochastic processes; Exercises
- Chapter 7. CHARACTERIZATION OF THE NORMAL DISTRIBUTION BY PROPERTIES OF INFINITE SUMS OF RANDOM VARIABLES7.1. Identically distributed linear forms; 7.2. A linear form and a monomial having the same distribution; 7.3. Independently distributed infinite sums; Exercises; Chapter 8. CHARACTERIZATION OF SOME STOCHASTIC PROCESSES; 8.1. Independence and a regression property of two stochastic integrals; 8.2. Identically distributed stochastic integrals; 8.3. Identity of the distribution of a stochastic integral and the increment of a process; 8.4. Characterization of stable processes; Exercises