An introduction to probability theory and its applications. Volume II

Second Ed.

New York

1971

669 S.

Bandaufführung

0-471-25709-5

117400

When this book was first conceived (more than 25 years ago) few mathematicians outside the Soviet Union recognized probability as a legitimate branch of mathematics. Applications were limited in scope, and the treatment of individual problems often led to incredible complications. Under these circumstances the book could not be written for an existing audience, or to satisfy conscious needs. The hope was rather to attract attention to little-known aspects of probability, to forge links between various parts, to develop unified methods, and to point to potential applications. Because of a growing interest in probability, the book found unexpectedly many users outside mathematical disciplines. Its widespread use was understandable as long as its point of view was new and its materials was not otherwise available. But the popularity seems to persists even now, when the contents of most chapters are available in specialized works streamlined for particular needs. For this reason the character of the book remains unchanged in the new edition. I hope that it will continue to serve a variety of needs and, in particular, that it will continue to find readers who read it merely for enjoyment and enlightenment. Throughout the years I was the grateful recipient of many communications from users, and these led to various improvements. Many sections were rewritten to facilitate study. Reading is also improved by a better typeface and the superior editing job by Mrs. H. McDougal: although a professional editor she has preserved a feeling for the requirements of readers and reason. The greates change is in chapter III. This chapter was introduced only in the second edition, which was in fact motivated principally by the unexpected discovery that its enticing material could be treated by elementary methods. But this treatment still depended on combinatorial artifices which have now been replaced by simpler and more natural probabilistic arguments. In essence this new chapter is new. Most conspicuous among other additions are the new sections on branching processes, on Markov chains, and on the DeMoivre-Laplace theorem. Chapter XIII has been rearranged, and throughout the book there appear minor changes as well as new examples and problems.