隨機(jī)積分和微分方程

內(nèi)容概要

　　本書是第2版（全英文版）。第1版本的《隨機(jī)積分和微分方程》問世13年以來，有關(guān)這方面的書不斷涌現(xiàn)，特別是在數(shù)學(xué)金融方面具有很強(qiáng)應(yīng)用性的書更是發(fā)展迅速。然而沒有一本書是真正用函數(shù)解析法來表達(dá)半鞅和隨機(jī)積分，這使得新的方法并沒有得到很好的應(yīng)用。盡管這本書不再適合稱其為一種新的方法。然而新版本的及時(shí)出現(xiàn)，在很大程度上完善了原版本。　　這版較第1版做了一些調(diào)整，并且增加了不少新的內(nèi)容。第3章增加了停時(shí)的分類和Bichteler-Dellacherie定理；第4張?jiān)黾恿索北硎镜腏acod-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練習(xí)，這些可以作為學(xué)習(xí)本教材的很好的補(bǔ)充。

作者簡(jiǎn)介

作者：(美國(guó))普若特(Protter P.E)

書籍目錄

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

編輯推薦

《隨機(jī)積分和微分方程(第2版)》是真正用函數(shù)解析法來表達(dá)半鞅和隨機(jī)積分，這使得新的方法并沒有得到很好的應(yīng)用。盡管這《隨機(jī)積分和微分方程(第2版)》不再適合稱其為一種新的方法。然而新版本的及時(shí)出現(xiàn)，在很大程度上完善了原版本。

圖書封面

圖書標(biāo)簽Tags

無

評(píng)論、評(píng)分、閱讀與下載

---

    隨機(jī)積分和微分方程 PDF格式下載

---