概率论 第2卷(英文版)

这是一套公认的概率论经典教科书，可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的专家，学者经常使用的参考书。在这套书的第4版中增加了距离空间测定，随机游动，布朗运动及不变原理，后两部门尤为精彩。

This book is intended as a text for graduate sudents and as a reference for workers in Probability and Statistics. The prerequisite is honest calculus. The material covered in Parts Two to Five inclusive requires about three to four semesters of graduate study. The introductory part may serve as a text for an undergraduate course in elementary probability theory.

　　本书为英文版。

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
CHATPER IX:FROM INDERENDENCE TO DEPENDENXE
31.CENTRAL ASYMPTOTIC PRAOBLEM
31.1 Comparison of laws
31.2 Compaison of summands
31.3 Weighted prob.laws
32.CENTERINGS MARTINGALES,AND A.S.CONVERGENCE
32.1 Centerings
32.2 Martingales:generanlities
……
CHPATER X:ERGODIC THEOREMS
CHAPTER XI:SECOND ORDER PROPERTIES
PART FIVE:ELEMENSTS OF RANDOM ANALYSIS
CHAPTER XII:FOUNDATIONS MARTINGLES AND DECOMPABLTY
CHAPTER XIII:BROWNIAN MOTON AND LIMIT DISTRIBUTIONS
CHAPTER XIV:MARKOV PROCESSES
BIBLEOGRAPHY
INDEX

PREFACE TO THE FOURTH EDITION 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 ..