內容簡介
《隨機積分和微分方程(第2版)》較第1版做了一些調整，並且增加了不少新的內容。第3章增加了停時的分類和Bichteler-Dellacherie定理；第4張增加了鞅表示的Jacod-Yor定理、鞅表示的例子以及Sigma鞅；增加了新的一章第6章。並且每章的後面增加了不少練習，這些可以作為學習本教材的很好的補充。第1版本的《隨機積分和微分方程》問世13年以來，有關這方面的書不斷湧現，特別是在數學金融方面具有很強套用性的書更是發展迅速。
作者簡介
作者：(美國)普若特(ProtterP.E)
目錄
Introduction
1 Preliminaries
1 Basic Definitions and Notation
3 ThePoisson processand 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 forpredictableIntegrands
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
11eclecticUseful 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
