概率论 第2卷 第4版 英文版PDF|Epub|txt|kindle电子书版本网盘下载

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PART FOUR:DEPENDENCE3

CHAPTER Ⅷ:CONDITIONING3

27．ONCEPT OF CONDITIONING3

27.1 Elementary case3

27.2 General case7

27.3 Conditional expectation given a function8

27.4 Relative conditional expectations and sufficient σ-fields10

28．ROPERTIES OF CONDITIONING13

28.1 Expectation properties13

28.2 Smoothing properties15

28.3 Concepts of conditional independence and of chains17

29．REGULAR PR.FUNCTIONS19

29.1 Regularity and integration19

29.2 Decomposition of regular c.pr.'s given separable σ-fields21

30．CONDITIONAL DISTRIBUTIONS24

30.1 Definitions and restricted integration24

30.2 Existence26

30.3 Chains;the elementary case31

COMPLEMENTS AND DETAILS36

CHAPTER Ⅸ:FROM INDEPENDENCE TO DEPENDENCE37

31．CENTRAL ASYMPTOTIC PROBLEM37

31.1 Comparison of laws38

31.2 Comparison ofsummands41

31.3 Weighted prob.laws44

32．CENTERINGS,MARTINGALES,AND A.S.CONVERGENCE51

32.1 Centerings51

32.3 Martingales:generalities54

32.3 Martingales:convergence and closure57

32.4 Applications63

32.5 Indefinite expectations and a.s.convergence67

COMPLEMENTS AND DETAILS73

CHAPTER Ⅹ: ERGODIC THEOREMS77

33．TRANSLATION OF SEQUENCES;BASIC ERGODIC THEOREM AND77

STATIONARITY77

33.1 Phenomenological origin77

33.2 Basic ergodic inequality79

33.3 Stationarity83

33.4 Applications;ergodic hypothesis and independence89

33.5 Applications;stationary chains90

34．ERGODIC THEOREMS AND Lr-SPACES96

34.1 Translations and their extensions96

34.2 A.s.ergodic theorem98

34.3 Ergodic theorems on spaces Lr101

35．ERGODIC THEOREMS ON BANACH SPACES106

35.1 Norms ergodic theorem106

35.2 Uniform norms ergodic theorems110

35.3 Application to constant chains114

COMPLEMENTS AND DETAILS118

CHAPTER Ⅺ:SECOND ORDER PROPERTIES121

36．ORTHOGONALITY121

36.1 Orthogonal r.v.'s; convergence and stability122

36.2 Elementary orthogonal decomposition125

36.3 Projection,conditioning,and normality128

37．SECOND ORDER RANDOM FUNCTIONS130

37.1 Covariances131

37.2 Calculus in q.m.;continuity and differentiation135

37.3 Calculus in q.m.;integration137

37.4 Fourier-Stieltjes transforms in q.m140

37.5 Orthogonal decompositions143

37.6 Normality and almost-sure properties151

37.7 A.s.stability152

COMPLEMENTS AND DETAILS156

PART FIVE: ELEMENTS OF RANDOM ANALYSIS163

CHAPTER Ⅻ: FOUNDATIONS;MARTINGALES AND DECOMPOSABILITY163

38．FOUNDATIONS163

38.1 Generalities164

38.2 Separability170

38.3 Sample continuity179

38.4 Random times188

39．MARTINGALES193

39.1 Closure and limits194

39.2 Martingale times and stopping207

40．DECOMPOSABILITY212

40.1 Generalities212

40.2 Three parts decomposition216

40.3 Infinite decomposability;normal and Poisson cases221

COMPLEMENTS AND DETAILS231

CHAPTER ⅩⅢ: BROWNIAN MOTION AND LIMIT DISTRIBUTIONS235

41．BROWNIAN MOTION235

41.1 Origins235

41.2 Definitions and relevant properties237

41.3 Brownian sample oscillations246

41.4 Brownian times and functionals254

42．LIMIT DISTRIBUTIONS263

42.1 Pr.'s on ？264

42.2 Limit distributions on ？268

42.3 Limit distributions;Brownian embedding271

42.4 Some specific functionals278

Complements and Details281

CHAPTER ⅩⅣ: MARKOV PROCESSES289

43．MARKOV DEPENDENCE289

43.1 Markov property289

43.2 Regular Markov processes294

43.4 Stationarity301

43.4 Strong Markov property304

44．TIME-CONTINUOUS TRANSITION PROBABILITIES310

44.1 Differentiation of tr.pr.'s312

44.2 Sample functions behavior321

45．MARKOV SEMI-GROUPS331

45.1 Generalities331

45.2 Analysis of semi-groups336

45.3 Markov processes and semi-groups346

46．SAMPLE CONTINUITY AND DIFFUSION OPERATORS357

46.1 Strong Markov property and sample rightcontinuity357

46.2 Extended infinitesimal operator366

46.3 One-dimensional diffusion operator374

COMPLEMENTS AND DETAILS381

BIBLIOGRAPHY384

INDEX391