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| 內容簡介： |
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《随机过程用的极限定理(第2版)(英文)》讲述Apart from correcting a number of printing mistakes,and some mathematical inaccuracies as well,this second edition contains some new material: indeed,during the fifteen years elapsed since the first edition came out,a large number of new results concerning limit theorems have of course been proved by many authors,and more generally mathematical life has been going on.This gave us the feeling that some of the material in the first edition was perhaps not as important as we thought at the time,while there were some neglected topics which have in fact proved to be very useful in various applications.So perhaps a totally new book would have been a good thing to write.Our natural laziness prevented us to do that,but we have felt compelled to fill in the most evident holes in this book.This has been done in the most painless way for us,and also for the reader acquainted with the first edition （at least we hope so ...）.That is all new material has been added at the end of preexisting chapters.
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| 目錄：
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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
……
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