Stochastic processes. Paperback edition. (English) Zbl 0696.60003

Doob, Joseph L.

Wiley Classics Library; A Wiley-Interscience Publication. New York etc.: John Wiley & Sons Ltd. vii, 654 p. £26.80 (1990).

The monograph is an unchanged paperback edition of the author’s famous book which appeared in 1953 (see Zbl 0053.26802). The 1953 edition was the first comprehensive treatment of stochastic processes in English language and is still widely used as a reference by researchers as well as an introductory book to the subject. Even though background material on probability and measure theory is presented in the first chapter and the supplement a student with no prior knowledge in these fields will usually find it hard to follow.
The main topics are Markov processes, martingales and strict and second order stationary processes. Both discrete and continuous parameter processes are treated. The author presents the spectral theory of scalar weakly stationary processes in detail and applies it to the linear least squares prediction problem. Of course the subjects treated in the book have undergone a dramatic development in the past almost forty years and some notions etc. are no longer used today or have a different meaning (e.g. Doobs “semimartingale” is nowadays called “submartingale”).

Reviewer: Michael Scheutzow (Berlin)

MSC:

60-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60G42	Martingales with discrete parameter
60G44	Martingales with continuous parameter
60J25	Continuous-time Markov processes on general state spaces
60G05	Foundations of stochastic processes
60G12	General second-order stochastic processes
60G25	Prediction theory (aspects of stochastic processes)

Keywords:

prediction; stochastic processes; martingales; strict and second order stationary processes; weakly stationary

Citations:

Zbl 0053.26802