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概率论教程PDF|Epub|txt|kindle电子书版本网盘下载
- （德）凯兰克著 著
- 出版社： 北京：世界图书北京出版公司
- ISBN：9787510044113
- 出版时间：2012
- 标注页数：621页
- 文件大小：105MB
- 文件页数：635页
- 主题词：概率论－教材－英文
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图书目录
1 Basic Measure Theory1
1.1 Classes of Sets1
1.2 Set Functions12
1.3 The Measure Extension Theorem18
1.4 Measurable Maps34
1.5 Random Variables43
2 Independence49
2.1 Independence ofEvents49
2.2 Independent Random Variables56
2.3 Kolmogorov's 0-1 Law63
2.4 Example:Percolation66
3 Generating Functions77
3.1 Definition and Examples77
3.2 Poisson Approximation80
3.3 Branching Processes82
4 The Integral85
4.1 Construction and Simple Properties85
4.2 Monotone Convergence and Fatou's Lemma93
4.3 Lebesgue Integral versus Riemann Integral95
5 Moments and Laws ofLarge Numbers101
5.1 Moments101
5.2 Weak Law of Large Numbers108
5.3 Strong Law of Large Numbers111
5.4 Speed of Convergence in the Strong LLN119
5.5 The Poisson Process123
6 Convergence Theorems129
6.1 Almost Sure and Measure Convergence129
6.2 Uniform Integrability134
6.3 Exchanging Integral and Differentiation140
7 Lp-Spaces and the Radon-Nikodym Theorem143
7.1 Definitions143
7.2 Inequalities and the Fischer-Riesz Theorem145
7.3 Hilbert Spaces151
7.4 Lebesgue's Decomposition Theorem154
7.5 Supplement:Signed Measures158
7.6 Supplement:Dual Spaces165
8 Conditional Expectations169
8.1 Elementary Conditional Probabilities169
8.2 Conditional Expectations173
8.3 Regular Conditional Distribution179
9 Martingales189
9.1 Processes,Filtrations,Stopping Times189
9.2 Martingales194
9.3 Discrete Stochastic Integral198
9.4 Discrete Martingale Representation Theorem and the CRR Model200
10 Optional Sampling Theorems205
10.1 Doob Decomposition and Square Variation205
10.2 Optional Sampling and Optional Stopping209
10.3 Uniform Integrability and Optional Sampling214
11 Martingale Convergence Theorems and Their Applications217
11.1 Doob's Inequality217
11.2 Martingale Convergence Theorems219
11.3 Example:Branching Process228
12 Backwards Martingales and Exchangeability231
12.1 Exchangeable Families of Random Variables231
12.2 Backwards Martingales236
12.3 De Finetti's Theorem239
13 Convergence of Measures245
13.1 A Topology Primer245
13.2 Weak and Vague Convergence251
13.3 Prohorov's Theorem259
13.4 Application:A Fresh Look at de Finetti's Theorem268
14 Probability Measures on Product Spaces271
14.1 Product Spaces272
14.2 Finite Products and Transition Kernels275
14.3 Kolmogorov's Extension Theorem283
14.4 Markov Semigroups288
15 Characteristic Functions and the Central Limit Theorem293
15.1 Separating Classes of Functions293
15.2 Characteristic Functions:Examples300
15.3 Lévy's Continuity Theorem307
15.4 Characteristic Functions and Moments312
15.5 The Central Limit Theorem317
15.6 Multidimensional Central Limit Theorem324
16 Infinitely Divisible Distributions327
16.1 Lévy-Khinchin Formula327
16.2 Stable Distributions339
17 Markov Chains345
17.1 Definitions and Construction345
17.2 Discrete Markov Chains:Examples352
17.3 Discrcte Markov Processes in Continuous Time356
17.4 Discrete Markov Chains:Recurrence and Transience361
17.5 Application:Recurrence and Transience of Random Walks365
17.6 Invariant Distributions372
18 Convergence of Markov Chains379
18.1 Periodicity of Markov Chains379
18.2 Coupling and Convergence Theorem383
18.3 Markov Chain Monte Carlo Method390
18.4 Speed of Convergence398
19 Markov Chains and Electrical Networks403
19.1 Harmonic Functions404
19.2 Reversible Markov Chains407
19.3 Finite Electrical Networks408
19.4 Recurrence and Transience414
19.5 Network Reduction421
19.6 Random Walk in a Random Environment427
20 Ergodic Theory431
20.1 Definitions431
20.2 Ergodic Theorems435
20.3 Examples437
20.4 Application:Recurrence of Random Walks439
20.5 Mixing442
21 Brownian Motion447
21.1 Continuous Versions447
21.2 Construction and Path Properties454
21.3 Strong Markov Property459
21.4 Supplement:Feller Processes462
21.5 Construction via L2-Approximation465
21.6 The Space C([0,∞))469
21.7 Convergence of Probability Measures on C([0,∞))471
21.8 Donsker's Theorem474
21.9 Pathwise Convergence of Branching Processes477
21.10 Square Variation and Local Martingales483
22 Law of the Iterated Logarithm495
22.1 Iterated Logarithm for the Brownian Motion495
22.2 Skorohod's Embedding Theorem498
22.3 Hartman-Wintner Theorem503
23 Large Deviations505
23.1 Cramér's Theorem506
23.2 Large Deviations Principle510
23.3 Sanov's Theorem514
23.4 Varadhan's Lemma and Free Energy519
24 The Poisson Point Process525
24.1 Random Measures525
24.2 Properties of the Poisson Point Process529
24.3 The Poisson-Dirichlet Distribution535
25 The It？ Integral543
25.1 It？ Integral with Respect to Brownian Motion543
25.2 It？ Integral with Respect to Diffusions551
25.3 The It？ Formula554
25.4 Dirichiet Problem and Brownian Motion562
25.5 Recurrence and Transience of Brownian Motion564
26 Stochastic Differential Equations567
26.1 Strong Solutions567
26.2 Weak Solutions and the Martingale Problem576
26.3 Weak Uniqueness via Duality583
References591
Notation Index599
Name Index603
Subject Index607