隨機過程用的極限定理 第2版 英文

隨機過程用的極限定理 第2版 英文
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內容簡介

講述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.
 

目錄

Chapter Ⅰ The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals
1.Stochastic Basis, Stopping Times, Optional a -Field, Martingales
a.Stochastic Basis
b.Stopping Times
c.The Optional σ-Field
d.The Localization Procedure
e.Martingales
f.The Discrete Case
2.Predictable σ-Field, Predictable Times
a.The Predictable σ-Field
b.Predictable Times
c.Totally Inaccessible Stopping Times
d.Predictable Projection
e.The Discrete Case
3.Increasing Processes
a.Basic Properties
b.Doob-Meyer Decomposition and Compensators of Increasing Processes
c.Lenglart Domination Property
d.The Discrete Case
4.Semimartingales and Stochastic Integrals
a.Locally Square-Integrable Martingales
b.Decompositions of a Local Martingale
c.Semimartingales
d.Construction of the Stochastic Integral
e.Quadratic Variation of a Semimartingale and Ito’’s Formula
f.Doleans-Dade Exponential Formula
g.The Discrete Case

Chapter Ⅱ Characteristics of Semimartingales and Processes with Independent Increments
1.Random Measures
1a.General Random Measures
1b.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
……
Chapter Ⅳ Bellinger Processes, Absolute Continuity
Chapter Ⅴ Contiguity, Entire Separation, Convergence in Variation
Chapter Ⅵ Skorokhod Topology and Convergence of Processes
Chapter Ⅶ Convergence of Processes with Independent Increments
Chapter Ⅷ Convergence to a Process with Independent Increments
Chapter Ⅸ Convergence to a Semimartingale
Chapter Ⅹ Limit Theorems, Density Processes and Contiguity Bibliographical Comments
References
Index of Symbols
Index of Terminology
Index of Topics
Index of Conditions for Limit Theorems
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