随机积分和微分方程（第2版）

　　本书是第2版（全英文版）。第1版本的《随机积分和微分方程》问世13年以来，有关这方面的书不断涌现，特别是在数学金融方面具有很强应用性的书更是发展迅速。然而没有一本书是真正用函数解析法来表达半鞅和随机积分，这使得新的方法并没有得到很好的应用。尽管这本书不再适合称其为一种新的方法。然而新版本的及时出现，在很大程度上完善了原版本。这版较第1版做了一些调整，并且增加了不少新的内容。第3章增加了停时的分类和Bichteler-Dellacherie定理；第4张增加了鞅表示的Jacod-Yor定理、鞅表示的例子以及Sigma鞅；增加了新的一章第6章。并且每章的后面增加了不少练习，这些可以作为学习本教材的很好的补充。

暂缺《随机积分和微分方程（第2版）》作者简介

Introduction
1 Preliminaries
1 Basic Definitions and Notation
2 Martingales
3 The Poisson Process and Brownian Motion
4 Levv Processes
5 Why the Usual Hypotheses?
6 Local Martingales
7 Stieltjes Integration and Change of Variables
8 Naive Stochastic Integration is Impossible
Bibliographic Notes
Exercises for Chapter 1
2 Semimartingales and Stochastic Integrals
1 Introduction to Semimartingales
2 Stability Properties of Semimartingales
3 Elementary Examples of Semimartingales
4 Stochastic Integrals
5 Properties of Stochastic Integrals
6 The Quadratic Variation of a Semimartingale
7 Ito's Formula (Change of Variables)
8 Applications of Ito's Formula
Bibliographic Notes
Exercises for Chapter 2
3 Semimartingales and Decomposable Processes
1 Introduction
2 The Classification of Stopping Times
3 The Doob-Meyer Decompositions
4 Quasimartingales
5 Compensators
6 The Fundamental Theorem of Local Martingales
7 Classical Semimartingales
8 Girsanov's Theorem
9 The Bichteler-Dellacherie Theorem
Bibliographic Notes
Exercises for Chapter 3
4 General Stochastic Integration and Local Times
1 Introduction
2 Stochastic Integration for Predictable Integrands
3 Martingale Representation
4 Martingale Duality and the Jacod-Yor Theorem on
Martingale Representation
5 Examples of Martingale Representation
6 Stochastic Integration Depending on a Parameter
7 Local Times
8 Az6ma's Martingale
9 Sigma Martingales
Bibliographic Notes
Exercises for Chapter 4
5 Stochastic Differential Equations
1 Introduction
2 The H___p Norms for Semimartingales
3 Existence and Uniqueness of Solutions
4 Stability of Stochastic Differential Equations
5 Fisk-Stratonovich Integrals and Differential Equations
6 The Markov Nature of Solutions
7 Flows of Stochastic Differential Equations: Continuity and
Differentiability
8 Flows as Diffeomorphisms: The Continuous Case
9 General Stochastic Exponentials and Linear Equations
10 Flows as Diffeomorphisms: The General Case
11 Eclectic Useful Results on Stochastic Differential Equations
Bibliographic Notes
Exercises for Chapter 5
6 Expansion of Filtrations
1 Introduction
2 Initial Expansions
3 Progressive Expansions
4 Time Reversal
Bibliographic Notes
Exercises for Chapter 6
References
Subject Index