- 概率论(第2卷第4版影印版)(英文版)
- - 作者：(美)M.洛易甫
  - 出版社：世界图书出版公司
  - ISBN：9787519255794
  - 出版日期：2019/03/01
  - 页数：413
- 售价：47.6

内容大纲
本书被公认为是一套概率论方面的标准经典教科书，供高年级大学生和研究生使用，同时也是概率论和统计学方面研究人员经常使用的参考书。本书把概率论建立在严格的逻辑基础上，理论体系完整。第2卷包括两部分内容，涉及条件运算及独立随机变量和极限性质的相依性、二阶随机函数、随机分析的基本概念以及鞅、可分解性、随机函数的马尔可夫型等。读者对象：数学及相关专业的研究生。
作者介绍
目录
PART FOUR: DEPENDENCE
  CHAPTER Ⅷ: CONDITIONING
    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
    σ-fiields
    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 summands
    "31.3  Weighted prob. laws
    32. CENTERINGS, MARTINGALES, AND A.$. CONVERGENCE
    32.1  Centerings
    32.3  Martingales: generalities
    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 AN
    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 Lt-SPACES
    *34.1  Translations and their extensions
    *34.2  A.s. ergodic theorem
    *34.3  Ergodic theorems on spaces L
    *35. ERGODIC THEOREMS ON BANACH SPACES
    *35.1  Norms crgodic 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  Covarianccs
    37.2  Calculus in q.m.; continuity and differentiation
    37.3  Calculus in q.m.; integration
    37.4  Fourier-Stichjes 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
    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
  CHAPTER 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.'son
    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
    44. TIME-CONTINUOUS TRANSITION 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 CONTINUITY 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

内容大纲

作者介绍

目录

同类热销排行榜

推荐书目