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随机积分导论 第2版PDF|Epub|txt|kindle电子书版本下载
- （美）钟开莱（Chung K. L.），R. J. Williams著 著
- 出版社： 北京;西安：世界图书出版公司出版社
- ISBN：9787510070259
- 出版时间：2014
- 标注页数：277页
- 文件大小：36MB
- 文件页数：295页
- 主题词：随机积分－英文
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图书目录
1．PRELIMINARIES1
1.1 Notations and Conventions1
1.2 Measurability,Lp Spaces and Monotone Class Theorems2
1.3 Functions of Bounded Variation and Stieltjes Integrals4
1.4 Probability Space,Random Variables,Filtration6
1.5 Convergence,Conditioning7
1.6 Stochastic Processes8
1.7 Optional Times9
1.8 Two Canonical Processes10
1.9 Martingales13
1.10 Local Martingales18
1.11 Exercises21
2．DEFINITION OF THE STOCHASTIC INTEGRAL23
2.1 Introduction23
2.2 Predictable Sets and Processes25
2.3 Stochastic Intervals26
2.4 Measure on the Predictable Sets32
2.5 Definition of the Stochastic Integral34
2.6 Extension to Local Integrators and Integrands43
2.7 Substitution Formula48
2.8 A Sufficient Condition for Extendability of λz50
2.9 Exercises54
3．EXTENSION OF THE PREDICTABLE INTEGRANDS57
3.1 Introduction57
3.2 Relationship between P,O,and Adapted Processes57
3.3 Extension of the Integrands63
3.4 A Historical Note71
3.5 Exercises73
4．QUADRATIC VARIATION PROCESS75
4.1 Introduction75
4.2 Definition and Characterization of Quadratic Variation75
4.3 Properties of Quadratic Variation for an L2-martingale79
4.4 Direct Definition of μM82
4.5 Decomposition of(M)286
4.6 A Limit Theorem89
4.7 Exercises90
5．THE ITO FORMULA93
5.1 Introduction93
5.2 One-dimensional It？ Formula94
5.3 Mutual Variation Process99
5.4 Multi-dimensional It？ Formula109
5.5 Exercises112
6．APPLICATIONS OF THE ITO FORMULA117
6.1 Characterization of Brownian Motion117
6.2 Exponential Processes120
6.3 A Family of Martingales Generated by M123
6.4 Feynman-Kac Functional and the Schr？dinger Equation128
6.5 Exercises136
7．LOCAL TIME AND TANAKA'S FORMULA141
7.1 Introduction141
7.2 Local Time142
7.3 Tanaka's Formula150
7.4 Proof of Lemma 7.2153
7.5 Exercises155
8．REFLECTED BROWNIAN MOTIONS157
8.1 Introduction157
8.2 Brownian Motion Reflected at Zero158
8.3 Analytical Theory of Z via the It？ Formula161
8.4 Approximations in Storage Theory163
8.5 Reflected Brownian Motions in a Wedge174
8.6 Alternative Derivation of Equation(8.7)178
8.7 Exercises181
9．GENERALIZED ITO FORMULA,CHANGE OF TIME AND MEASURE183
9.1 Introduction183
9.2 Generalized It？ Formula184
9.3 Change of Time187
9.4 Change of Measure197
9.5 Exercises214
10．STOCHASTIC DIFFERENTIAL EQUATIONS217
10.1 Introduction217
10.2 Existence and Uniqueness for Lipschitz Coefficients220
10.3 Strong Markov Property of the Solution235
10.4 Strong and Weak Solutions243
10.5 Examples252
10.6 Exercises262
REFERENCES265
INDEX273