随机过程用的极限定理 第2版

Chapter I. The General Theory of Stochastic Processes,
Semimartingales and Stochastic Integrals
1. Stochastic Basis, Stopping Times, Optional
a-Field,Martingales
　1a. Stochastic Basis
　lb. Stopping Times
　lc. The Optional a-Field
　ld. The Localization Procedure
　1e. Martingales
　1f. The Discrete Case
2. Predictable a-Field, Predictable Times
　2a. The Predictable a-Field
　2b. Predictable Times
　2c. Totally Inaccessible Stopping Times
　2d. Predictable Projection
　2e. The Discrete Case
3. Increasing Processes　
　3a. Basic Properties
　3b. Do, b-Meyer Decomposition and Compensatorsof Increasing
Processes
　3c. Lenglart Domination Property
　3d. The Discrete Case
4. Semimartingales and Stochastic Integrals
　4a. Locally Square-Integrable Martingales
　4b. Decompositions of a Local Martingale
　4c. Semimartingales
　4d. Construction of the Stochastic Integral
　4e. Quadratic Variation ofa Semimartingale and Ito’s Formula
　4f. Dol6ans-Dade Exponential Formula
　4g. The Discrete Case
Chapter II. Characteristics of Semimartingales and Processes　with
Independent Increments
1. Random Measures
　1a. General Random Measures
　lb. Integer-Valued Random Measures
　1c. A Fundamental Example: Poisson Measures
　1d. Stochastic Integral with Respect to a Random Measure
2. Characteristics of Semimartingales
　2a. Definition of the Characteristics
　2b. Integrability and Characteristics
　2c. A Canonical Representation for Semimartingales
　2d. Characteristics and Exponential Formula
3. Some Examples
　3a. The Discrete Case
　3b. More on the Discrete Case
　3c. The “One-Point” Point Process and Empirical Processes
4. Semimartingales with Independent Increments
　4a. Wiener Processes
　4b. Poisson Processes and Poisson Random Measures
　4c. Processes with Independent Increments and
Semimartingales
　4d. Gaussian Martingales
5. Processes with Independent Increments
　Which Are Not Semimartingales
　5a. The Results
　5b. The Proofs
6. Processes with Conditionally Independent Increments
7. Progressive Conditional Continuous PIIs
8. Semimartingales, Stochastic Exponential and Stochastic
Logarithm.
　8a. More About Stochastic Exponential and Stochastic
Logarithm.
　8b. Multiplicative Decompositions and
Exponentially　Special　Semimartingales
Chapter III. Martingale Problems and Changes of Measures
1. Martingale Problems and Point Processes
　1a. General Martingale Problems
　1b. Martingale Problems and Random Measures
　1c. Point Processes and Multivariate Point Processes
……