随机积分和微分方程

内容概要

作者：(美国)普若特(Protter P.E)

书籍目录

Introduction1 Preliminaries1 Basic Definitions and Notation2 Martingales3 The Poisson Process and Brownian Motion4 Levv Processes5 Why the Usual Hypotheses?6 Local Martingales7 Stieltjes Integration and Change of Variables8 Naive Stochastic Integration is ImpossibleBibliographic NotesExercises for Chapter 12 Semimartingales and Stochastic Integrals1 Introduction to Semimartingales2 Stability Properties of Semimartingales3 Elementary Examples of Semimartingales4 Stochastic Integrals5 Properties of Stochastic Integrals6 The Quadratic Variation of a Semimartingale7 Ito's Formula (Change of Variables)8 Applications of Ito's FormulaBibliographic NotesExercises for Chapter 23 Semimartingales and Decomposable Processes1 Introduction2 The Classification of Stopping Times3 The Doob-Meyer Decompositions4 Quasimartingales5 Compensators6 The Fundamental Theorem of Local Martingales7 Classical Semimartingales8 Girsanov's Theorem9 The Bichteler-Dellacherie TheoremBibliographic NotesExercises for Chapter 34 General Stochastic Integration and Local Times1 Introduction2 Stochastic Integration for Predictable Integrands3 Martingale Representation4 Martingale Duality and the Jacod-Yor Theorem onMartingale Representation5 Examples of Martingale Representation6 Stochastic Integration Depending on a Parameter7 Local Times8 Az6ma's Martingale9 Sigma MartingalesBibliographic NotesExercises for Chapter 45 Stochastic Differential Equations1 Introduction2 The H___p Norms for Semimartingales3 Existence and Uniqueness of Solutions4 Stability of Stochastic Differential Equations5 Fisk-Stratonovich Integrals and Differential Equations6 The Markov Nature of Solutions7 Flows of Stochastic Differential Equations: Continuity andDifferentiability8 Flows as Diffeomorphisms: The Continuous Case9 General Stochastic Exponentials and Linear Equations10 Flows as Diffeomorphisms: The General Case11 Eclectic Useful Results on Stochastic Differential EquationsBibliographic NotesExercises for Chapter 56 Expansion of Filtrations1 Introduction2 Initial Expansions3 Progressive Expansions4 Time ReversalBibliographic NotesExercises for Chapter 6ReferencesSubject Index

编辑推荐

《随机积分和微分方程(第2版)》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《随机积分和微分方程(第2版)》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。

作者简介

《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。

图书封面

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