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。

Introduction

Ⅰ 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 Ⅰ

Ⅱ 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 Ⅱ

Ⅲ 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 Ⅲ

Ⅳ 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 Ⅳ

Ⅴ Stochastic Differential Equations

 1 Introduction

 2 The Hp 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 Ⅴ

Ⅵ Expansion of Filtrations

 1 Introduction

 2 Initial Expansions

 3 Progressive Expansions

 4 Time Reversal

 Bibliographic Notes

 Exercises for Chapter Ⅵ

References

Subject Index