《隨機積分導論(第2版)(英文版)》由（美）鐘開萊著，是一部可讀性很強的講述隨機積分和隨機微分方程的入門教程。將基本理論和套用巧妙結合，非常適合學習過機率論知識的研究生，學習隨機積分。運用現代方法，隨機積分的定義是為了可料被積函式和局部鞅，緊接著是連續鞅的變分公式ITO變化。書中包括在布朗運動的描述、鞅的Hermite多項式、Feynman—Kac泛函和Schrodinger方程。這是第二版，討論了Cameron—Martin—Giranov變換，並且在最後一章引入隨機微分方程和一些學生用的練習。
基本介紹
- 書名：隨機積分導論
- 作者：鐘開萊 (K.L.Chung)
- 出版社：世界圖書出版公司北京公司
- 頁數：276頁
- 開本：24
- 品牌：世界圖書出版公司北京公司
- 外文名：Introduction to Stochastic Integration
- 類型：英語與其他外語
- 出版日期：2014年3月1日
- 語種：簡體中文, 英語
- ISBN：9787510070259
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《隨機積分導論(第2版)(英文版)》由世界圖書出版公司北京公司出版。
作者簡介
作者：（美國）鐘開萊（K.L.Chunk.） （美國）R.J.Williams
圖書目錄
Preface
Preface to the First Edition
Abbreviations and Symbols
1. Preliminaries
1.1 Notations And Conventions
1.2 Measurability, Lp Spaces And Monotone Class Theorems
1.3 Functions of Bounded Variation And Stieltjes Integrals
1.4 Probability Space, Random Variables, Filtration
1.5 Convergence, Conditioning
1.6 Stochastic Processes
1.7 Optional Times
1.8 Two Canonical Processes
1.9 Martingales
1.10 Local Martingales
1.11 Exercises
2. Definition of The Stochastic Integral
2.1 Introduction
2.2 Predictable Sets And Processes
2.3 Stochastic Intervals
2.4 Measure on The Predictable Sets
2.5 Definition of The Stochastic Integral
2.6 Extension To Local Integrators And Integrands
2.7 Substitution Formula
2.8 A Sufficient Condition for Extendability of Hz
2.9 Exercises
3. Extension of The Predictable Integrands
3.1 Introduction
3.2 Relationship Between P, O, And Adapted Processes
3.3 Extension of The Integrands
3.4 A Historical Note
3.5 Exercises
4. Quadratic Variation Process
4.1 Introduction
4.2 Definition And Characterization of Quadratic Variation
4.3 Properties of Quadratic Variation For An L2-Wartingale
4.4 Direct Definition of ΜM
4.5 Decomposition of （M）2
4.6 A Limit Theorem
4.7 Exercises
5. The Ito Formula
5.1 Introduction
5.2 One-Dimensional It5 Formula
5.3 Mutual Variation Process
5.4 Multi-Dimensional It5 Formula
5.5 Exercises
6. APPLICATIONS OF THE ITO FORMULA
6.1 Characterization of Brownian Motion
6.2 Exponential Processes
6.3 A Fami]y of Martingales Generated by M
6.4 Feynman-Kac Functional and the Schriodinger Equation
6.5 Exercises
7. LOCAL TIME AND TANAKA'S FORMULA
7.1 Introduction
7.2 Local Time
7.3 Tanala's Formula
7.4 Proof of Lemma 7.2
7.5 Exercises
8. REFLECTED BROWNIAN MOTIONS
8.1 Introduction
8.2 Brownian Motion Reflected at Zero
8.3 Analytical Theory of Z via the It5 Formula
8.4 Approximations in Storage Theory
8.5 Reflected Brownian Motions in a Wedge
8.6 Alternative Derivation of Equation (8.7)
8.7 Exercises
9. GENERALIZED ITO FORMULA, CHANGE OF TIME AND MEASURE
9.1 Introduction
9.2 Generalized Ito Formula
9.3 Change of Time
9.4 Change of Measure
9.5 Exercises
10. STOCHASTIC DIFFERENTIAL EQUATIONS
10.1 Introduction
10.2 Existence and Uniqueness for Lipschits Coefficients
10.3 Strong Markov Property of the Solution
10.4 Strong and Weak Solutions
10.5 Examples
10.6 Exercises
REFERENCES
INDEX
Preface to the First Edition
Abbreviations and Symbols
1. Preliminaries
1.1 Notations And Conventions
1.2 Measurability, Lp Spaces And Monotone Class Theorems
1.3 Functions of Bounded Variation And Stieltjes Integrals
1.4 Probability Space, Random Variables, Filtration
1.5 Convergence, Conditioning
1.6 Stochastic Processes
1.7 Optional Times
1.8 Two Canonical Processes
1.9 Martingales
1.10 Local Martingales
1.11 Exercises
2. Definition of The Stochastic Integral
2.1 Introduction
2.2 Predictable Sets And Processes
2.3 Stochastic Intervals
2.4 Measure on The Predictable Sets
2.5 Definition of The Stochastic Integral
2.6 Extension To Local Integrators And Integrands
2.7 Substitution Formula
2.8 A Sufficient Condition for Extendability of Hz
2.9 Exercises
3. Extension of The Predictable Integrands
3.1 Introduction
3.2 Relationship Between P, O, And Adapted Processes
3.3 Extension of The Integrands
3.4 A Historical Note
3.5 Exercises
4. Quadratic Variation Process
4.1 Introduction
4.2 Definition And Characterization of Quadratic Variation
4.3 Properties of Quadratic Variation For An L2-Wartingale
4.4 Direct Definition of ΜM
4.5 Decomposition of （M）2
4.6 A Limit Theorem
4.7 Exercises
5. The Ito Formula
5.1 Introduction
5.2 One-Dimensional It5 Formula
5.3 Mutual Variation Process
5.4 Multi-Dimensional It5 Formula
5.5 Exercises
6. APPLICATIONS OF THE ITO FORMULA
6.1 Characterization of Brownian Motion
6.2 Exponential Processes
6.3 A Fami]y of Martingales Generated by M
6.4 Feynman-Kac Functional and the Schriodinger Equation
6.5 Exercises
7. LOCAL TIME AND TANAKA'S FORMULA
7.1 Introduction
7.2 Local Time
7.3 Tanala's Formula
7.4 Proof of Lemma 7.2
7.5 Exercises
8. REFLECTED BROWNIAN MOTIONS
8.1 Introduction
8.2 Brownian Motion Reflected at Zero
8.3 Analytical Theory of Z via the It5 Formula
8.4 Approximations in Storage Theory
8.5 Reflected Brownian Motions in a Wedge
8.6 Alternative Derivation of Equation (8.7)
8.7 Exercises
9. GENERALIZED ITO FORMULA, CHANGE OF TIME AND MEASURE
9.1 Introduction
9.2 Generalized Ito Formula
9.3 Change of Time
9.4 Change of Measure
9.5 Exercises
10. STOCHASTIC DIFFERENTIAL EQUATIONS
10.1 Introduction
10.2 Existence and Uniqueness for Lipschits Coefficients
10.3 Strong Markov Property of the Solution
10.4 Strong and Weak Solutions
10.5 Examples
10.6 Exercises
REFERENCES
INDEX
