概率論（第1卷）

內(nèi)容概要

這是一套公認(rèn)的概率論經(jīng)典教科書，可供高年級(jí)大學(xué)生和研究生使用，同時(shí)也是概率論和統(tǒng)計(jì)學(xué)方面專家、學(xué)者經(jīng)常使用的參考書。在這套書的第4版中增加了距離空間測定、隨機(jī)游動(dòng)、布朗運(yùn)動(dòng)及不變原理，后兩部尤為精彩。

書籍目錄

INTRODUCTORY PART: ELEMENTARY PROBABILITY THEORY SECTION   Ⅰ.INTUITIVE BACKGROUND     1.Events     2.Random events and trials     3.Random variables   Ⅱ.AXIOMS； INDEPENDENCE AND THE BERNOULLI CASE     1.Axioms of the finite case     2.Simple random variables     3.Independence     4.Bernoulli case     5.Axioms for the countable case     6.Elementary random variables     7.Need for nonelementary random variables   Ⅲ.DEPENDENCE AND CHAINS     1.Conditional probabilities     2.Asymptotically Bernoullian case     3.Recurrence     4.Chain dependence     5.Types of states and asymptotic behavior     6.Motion of the system    7.Stationary chainsCOMLEMENTS AND DETAILSPART ONE:NOTIONS OF MEASURE THEORY  CHAPTERⅠ:SETS,SPACES,AND MEASURES    1.SETS,CLASSES,AND FUNCTIONS    2.TOPOLOGICAL SPACES    3.ADDITIVE SET FUNCTIONS    4.CONSTRUCTION OF MEASURES ONFIELDS  CHAPTERⅡ:MEASURABLE FUNCTIONS AND INTEGRATION    5.MEASURABLE FUNCTIONS    6.MEASURE AND CONVERGENCES    7.INTEGRATION    8.INDEFINITE INTEGRALS;ITERATED INTEGRALSPART TWO:GENERAL CONCEPTS AND TOOLS OF PROBABILITY THEORY  CHAPTERⅢ:PROBABILITY CONCEPTS    9.PROBABILITY SPACES AND RANDOM VARIABLES    10.PROBABILITY DISTRIBUTIONS  CHAPTERⅣ:DISTRIBUTION FUNCTIONS AND CHARACTERISTIC FUNCTIONNS    11.DISTRIBUTION FUNCTIONS    12.CONVERGENCE OF PROBABILITIES ON METRIC SPACES    13.CHARACTERISTIC FUNCTIONS AND DISTRIBUTION FUNCTIONS    14.PROBABILITY LAWS AND TYPES OF LAWS    15.NONNEGATIVE-DEFINITENESS;REGULARITYPART THREE:INDEPENDENCE  CHAPTERⅤ:SUMS OF INDEPENDENT RANDOM VARIABLES    16.CONCEPT OF INDEPENDENCE    17.CONVERGENCE AND STABILITY OF SUMS;CENTERING AT    18.CONVERGENCE AND SABILTIY OF SUMS;CENTERING AT    19.EXPONENTIAL BOUNDS AND NORMED SUMS  CHAPTERⅥ:ENTRAL LIMIT PROBLEM    20.DEGENERATE,NORMAL AND POISSON TYPES    21.EVOLUTION OF THE PROBLEM    22.CENTRAL LIMIT PROBLEM;THE CASE OF BOUNDED VARIANCES    23.SOLUTION OF THE ENTRAL LIMIT PROBLEM    24.NORMED SUMS  CHAPTERⅦ:INDEPENDENT IDENTICALLY DISTRIBUTED SUMMANDS    25.REGULAR VARIATION AND DOMAINS OF ATTRACTION    26.RANDOM WALKBIBLIOGRAPHYINDEX

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