Joseph L. Doob Bücher

The theory of stochastic processes has developed so much in the last twenty years that the need for a systematic account of the subject has been felt, particularly by students and instructors of probability. This book fills that need. While even elementary definitions and theorems are stated in detail, this is not recommended as a first text in probability and there has been no compromise with the mathematics of probability. Since readers complained that omission of certain mathematical detail increased the obscurity of the subject, the text contains various mathematical points that might otherwise seem extraneous. A supplement includes a treatment of the various aspects of measure theory. A chapter on the specialized problem of prediction theory has also been included and references to the literature and historical remarks have been collected in the Appendix.

This text is unique in accepting probability theory as an essential part of measure theory. Therefore, many examples are taken from probability, and probabilistic concepts such as independence and Markov processes are integrated into the text. Also, more attention than usual is paid to the role of algebras, and the metric defining the distance between sets as the measure of their symmetric difference is exploited more than is customary.