This fourth edition contains several additions. The main ones concern three closely related topics： Brownian motion， functional limit distributions， and random walks. Besides the power and ingenuity of their methods and the depth and beauty of their results， their importance is fast growing in Analysis as well as in theoretical and applied Probability. These additions increased the book to an unwieldy size and it had to be split into two volumes. About half of the first volume is devoted to an elementary introduction， then to mathematical foundations and basic probability concepts and tools. The second half is devoted to a detailed study of Independence which played and continues to play a central role both by itself and as a catalyst.
作者簡介
暫缺《概率論（第2卷 第4版）》作者簡介
圖書目錄
PART FOUR: DEPENDENCE CHAPTER VIII: CONDITIONING SECTION 27. CONCEPT OF CONDITIONING 27.1 Elementary case 27.2 General case 27.3 Conditional expectation given a function *27.4 Relative conditional expectations and sufficient a-fields 28. PROPERTIES OF CONDITIONING 28.1 Expectation properties 28.2 Smoothing properties *28.3 Concepts of conditional independence and of chains 29. REGULAR PR. FUNCTIONS 29.1 Regularity and integration *29.2 Decomposition of regular c.pr.''s given separable a-fields 30. CONDITIONAL DISTRIBUTIONS 30.1 Definitions and restricted integration 30.2 Existence 30.3 Chains; the elementary case COMPLEMENTS AND DETAILS CHAPTER IX: FROM INDEPENDENCE TO DEPENDENCE 31. CENTRAL ASYMPTOTIC PROBLEM 31.1 Comparison of laws 31.2 Comparison of surnmands 31.3 Weighted prob. laws 32. CENTERINGS, MARTINGALES, AND A.S. CONVERGENCE 32.1 Centerings 32.3 Martingales: generalities SECTION 32.3 Martingales: convergence and closure 32.4 Applications *32.5 Indefinite expectations and a.s. convergence COMPLEMENTS AND DETAILS CHAPTER X: ERGODIC THEOREMS 33. TRANSLATION OF SEQUENCES; BASIC ERGODIC THEOREM AND STATIONA RITY *33.1 Phenomenological origin 33.2 Basic ergodic inequality 33.3 Stationarity 33.4 Applications; ergodic hypothesis and independence *33.5 Applications; stationary chains *34. ERGODIC THEOREMS AND Lr-SPACES *34.1 Translations and their extensions *34.2 A.s. ergodic theorem *34.3 Ergodic theorems on spaces Lr *35. ERGODIC THEOREMS ON BANACH SPACES *35.1 Norms ergodic theorem *35.2 Uniform norms ergodic theorems *35.3 Application to constant chains COMPLEMENTS AND DETAILS CHAPTER XI: SECOND ORDER PROPERTIES 36. ORTHOGONALITY 36.1 Orthogonal r.v.''s; convergence and stability 36.2 Elementary orthogonal decomposition 36.3 Projection, conditioning, and normality 37. SECOND ORDER RANDOM FUNCTIONS 37.1 Covariances 37.2 Calculus in q.m.; continuity and differentiation 37.3 Calculus in q.m.; integration 37.4 Fourier-Stieltjes transforms in q.m. 37.5 Orthogonal decompositions 37.6 Normality and almost-sure properties 37.7 A.s. stability COMPLEMENTS AND DETAILS PART FIVE: ELEMENTS OF RANDOM ANALYSIS CHAPTER XII: FOUNDATIONS;MARTINGALES AND DECOMPOSABILITY SECTION 38. FOUNDATIONS 38.1 Generalities 38.2 Separability 38.3 Sample continuity 38.4 Random times 39. MARTINGALES 39.1 Closure and limits 39.2 Martingale times and stopping 40. DECOMPOSABILITY 40.1 Generalities 40.2 Three parts decomposition 40.3 Infinite decomposability; normal and Poisson cases COMPLEMENTS AND DETAILS CHAPTEK XIII: BROWNIAN MOTION AND LIMIT DISTRIBUTIONS 41. BROWNIAN MOTION 41.1 Origins 41.2 Definitions and relevant properties 41.3 Brownian sample oscillations 41.4 Brownian times and functionals 42. LIMIT DISTRIBUTIONS 42.1 Pr.''s on e 42.2 Limit distributions on e 42.3 Limit distributions; Brownian embedding 42.4 Some specific functionals Complements and Details CHAPTER XIV:MARKOV PROCESSES 43. MARKOV DEPENDENCE 43.1 Markov property 43.2 Regular Markov processes 43.4 Stationarity 43.4 Strong Markov property SECTION 44. TIME-CONTINUOUS TRANSlTION PROBABILITIES 44.1 Differentiation of tr. pr.''s 44.2 Sample functions behavior 45. MARKOV SEMI-GROUPS 45.1 Generalities 45.2 Analysis of semi-groups 45.3 Markov processes and semi-groups 46. SAMPLE COSTINUITY AND DIFFusioN OPERATORS 46.1 Strong Markov property and sample rightcontinuity 46.2 Extended infinitesimal operator 46.3 One-dimensional diffusion operator COMPLEMENTS AND DETAILS BIBLIOGRAPHY INDEX
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