目录 Introduction Ⅰ Preliminaries 1 Basic Definitions and Notation 2 Martingales 3 The Poison Process and Brownian Motion 4 Levy 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 Ⅰ Ⅱ 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 Ⅱ Ⅲ 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 Ⅲ Ⅳ 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 Azema's Martingale 9 Sigma Martingales Bibliographic Notes Exercises for Chapter Ⅳ Ⅴ Stochastic Differential Equations 1 Introduction 2 The Hp Norms for Semimartingales
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