Stochastic Processes

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.

Introduction and Probability Background. Definition of a Stochastic Process--Principal Classes. Processes with Mutually Independent Random Variables. Processes with Mutually Uncorrelated or Orthogonal Random Variables. Markov Processes--Discrete Parameter. Markov Processes--Continuous Parameter. Martingales. Processes with Independent Increments. Processes with Orthogonal Increments. Stationary Processes--Discrete Parameter. Stationary Processes--Continuous Parameter. Linear Least Squares Prediction--Stationary (Wide Sense) Processes. Supplement. Appendix. Bibliography. Index.