出版时间:2006-5 出版社:世界图书出版公司(此信息作废) 作者:爱卡拉察斯 页数:470
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前言
Two of the most fundamental concepts in the theory of stochastic processes are the Markov property and the martingale property.* This book is written for readers who are acquainted with both of these ideas in the discrete-time setting, and who now wish to explore stochastic processes in their continuoustime context. It has been our goal to write a systematic and thorough exposition of this subject, leading in many instances to the frontiers of knowledge.At the same time, we have endeavored to keep the mathematical prerequisites as low as pos..
内容概要
本书是Springer《数学研究生丛书》之113卷,是国内外公认的金融数学经典教材,各章有习题详解。本书初版于1988年,1991年出第2版,之后Springer已重印8次,本书是2005年的第8次重印版。
书籍目录
Preface Suggestions for the Reader Interdependence of the Chapters Frequently Used Notation CHAPTER 1 Martingales, Stopping Times, and Filtrations 1.1. Stochastic Processes and (y-Fields 1.2. Stopping Times 1.3. Continuous-Time Martingales 1.4. The Doob-Meyer Decomposition 1.5. Continuous, Square-Integrable Martingales 1.6. Solutions to Selected Problems 1.7. Notes CHAPTER 2 Brownian Motion 2.1. Introduction 2.2. First Construction of Brownian Motion 2.3. Second Construction of Brownian Motion 2.4. The Space C[0, ∞), Weak Convergence, and Wiener Measure 2.5. The Markov Property 2.6. The Strong Markov Property and the Reflection Principle 2.7. Brownian Filtrations 2.8. Computations Based on Passage Times 2.9. The Brownian Sample Paths 2.10. Solutions to Selected Problems 2.11. NotesCHAPTER 3 Stochastic Integration 3.1 Introduction 3.2 Construction of the Stochastic Integral 3.3 The Change-of-Variable Formula 3.4 Representations of Continuous Martingales in Terms of Brownian Motion ……CHAPTER 4 Brownian Motion and Partial Differential EquationsCHAPTER 5 Stochastic Differential EquationsCHAPTER 6 P.Levy's Theory of Brownian Local TimeBibliographyIndex
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