| 词条 | 随机积分和微分方程 |
| 释义 | 图书信息书名：随机积分和微分方程 出版社: 世界图书出版公司; 第2版 (2008年4月1日) 平装: 419页 正文语种: 英语 开本: 24 isbn: 9787506291972 条形码: 9787506291972 商品尺寸: 22 x 14.6 x 2.2 cm 商品重量: 558 g 品牌: 世界图书出版公司北京公司 内容简介《随机积分和微分方程(第2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。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。 作者简介作者：(美国)普若特(ProtterP.E) 目录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 |
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