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Foundations of stochastic analysis /
Foundations of Stochastic Analysis.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1981.
|
| Colección: | Probability and mathematical statistics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Foundations of Stochastic Analysis; Copyright Page; Dedication; Table of Contents; Preface; Chapter I. Introduction and Generalities; 1.1 INTRODUCING A STOCHASTIC PROCESS; 1.2 R�ESUM�E OF REAL ANALYSIS; 1.3 THE BASIC EXISTENCE THEOREM; 1.4 SOME RESULTS FROM ABSTRACT ANALYSIS AND VECTOR MEASURES; 1.5 REMARKS ON MEASURABILITY AND LOCALIZABILITY; Chapter II. Conditional Expectations and Probabilities; 2.1 INTRODUCTION OF THE CONCEPT; 2.2 SOME CHARACTERIZATIONS OF CONDITIONAL EXPECTATIONS; 2.3 CONDITIONAL PROBABILITIES; 2.4 SOME CHARACTERIZATIONS OF CONDITIONAL PROBABILITIES
- 2.5 RELATIONS WITH R�ENYI'S NEW AXIOMATIC APPROACH2.6 APPLICATIONS TO REYNOLDS OPERATORS; Chapter III. Projective and Direct Limits; 3.1 DEFINITION AND IMMEDIATE CONSEQUENCES; 3.2 SOME CHARACTERIZATIONS OF PROJECTIVE LIMITS; 3.3 DIRECT LIMITS AND A GENERALIZED KOLMOGOROV EXISTENCE THEOREM; 3.4 INFINITE PRODUCT CONDITIONAL PROBABILITY MEASURES; 3.5 A MULTIDIMENSIONAL EXTENSION; Chapter IV. Martingales and Likelihood Ratios; 4.1 DEFINITION AND FUNDAMENTAL INEQUALITIES; 4.2 CONVERGENCE THEORY; 4.3 EXTENSIONS TO INFINITE MEASURES; 4.4 APPLICATIONS TO LIKELIHOOD RATIOS; 4.5 ASYMPTOTIC MARTINGALES
- Chapter V. Abstract Martingales and Applications5.1 INTRODUCTION; 5.2 ABSTRACT MARTINGALES AND CONVERGENCE; 5.3 MARTINGALES AND ERGODIC THEORY; 5.4 A UNIFIED FORMULATION OF SOME ERGODIC AND MARTINGALE THEOREMS; 5.5 MARTINGALES IN HARMONIC ANALYSIS; Bibliography; Index; Probability and Mathematical Statistics