隨機積分和微分方程

《隨機積分和微分方程》是由普若特編寫,世界圖書出版公司出版的一本圖書。

基本信息

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

2martingales

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

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