CC/NUMBER 19
                                           This Week’s Citation Classic                                                      MAY 12, 1980
                                           Papoulis A. Probability, random variables, and stochastic processes. New York:
                                              McGraw Hill, 1965. 583 p.
                                              [ Department of Electrical Engineering, Polytechnic Institute of New York, Brooklyn,
                                              NY]
                                        Axiomatic development of the theory of               ‘Scientific theories deal with concepts, never
                                        probability and stochastic processes with            with reality. All theoretical results are derived
                                        emphasis on conceptual clarity is presented.         from certain axioms by deductive logic. The
                                        It includes: repeated trials and asymptotic          theories are so formulated as to correspond
                                        theorems, ergodicity, spectral analysis,             in some useful sense to the real world
                                        linear systems, estimation and filtering,            whatever that may mean. However, this
                                        normal and Markoff processes, Shot noise.            correspondence is approximate, and the
                                                  ® 
                                        [The SCI indicates that this book has been           physical justification of all theoretical
                                        cited over 995 times since 1965.]                    conclusions is based on some form of
                                                                                             inductive reasoning.’
                                                                                              “My second task was to simplify and unify
                                                                                             the treatment of applied topics: Poisson
                                                                                             processes, Brownian motion, thermal noise,
                                                                                             harmonic analysis. Such topics are
                                                     Athanasios Papoulis                     developed in specialized books where the
                                               Polytechnic Institute of New York             primary emphasis is on applications. I chose
                                                   Farmingdale, NY 11735                     a different approach: I tried to develop them
                                                                                             as illustrations of the general theory
                                                                      January 11, 1980       concentrating always on probabilistic
                                                                                             content and minimizing peripheral,
                                                                                             descriptive material.
                                                                                              “A typical illustration is the Wiener theory of
                                          “Probability is not a typical scientific           estimation. This topic, first published as a
                                        discipline. Students of the subject find the         classified report during the war, appeared in
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                                        definitions often ambiguous and they                 the open literature in a yellow monograph
                                        interpret the results not as manifestations of       known as the yellow peril because it was
                                        physical laws but rather as measures of our          written in a language that was foreign to
                                        ignorance. I wrote this book mainly because          most engineers. The importance of the
                                        I wanted to overcome the resulting                   theory was soon recognized and new
                                        skepticism.                                          applications were discussed in engineering
                                          “In my view, the book has been highly cited        texts. However, most treatments were based
                                        for two reasons: (1) It presents the theory of       essentially on the original derivations that
                                        probability as a deductive structure free from       involved advanced theory of functions,
                                        conceptual ambiguities. (2) It treats a              integral equations, and the calculus of
                                        variety of seemingly difficult concepts and          variations. Perhaps the main reason for my
                                        applications with clarity, simplicity, and           involvement with this book was my
                                        perspective.                                         conviction that  a simpler approach was
                                          “To achieve the above objectives, I stressed       possible. Starting from the estimation of one
                                        early in the book that probability, like any         random variable in terms of another, I
                                        other science, is a mental structure whose           formulated the ‘orthogonality principle’ and
                                        conclusions are based not on experience but          used it to solve a variety of estimation
                                        on logic. Departing from the tradition of            problems. The development is often
                                        technical books, I devoted the first chapter         heuristic but it leads to simple results. It is in
                                        on the philosophical meaning of probability          this sense characteristic of the entire book:
                                        to explaining the necessity for a clear              occasional sacrifice of mathematical rigor
                                        distinction between assumptions and                  for the sake of clarity, perspective, and
                                        deductions. The starting sentence of this            economy. The results were unexpected; they
                                        chapter is an indication of my approach:             are gratifying.”
                                        1.  Wiener N. Extrapolation, interpolation, and smoothing of stationary time series. New York: MIT  Press
                                           and John Wiley, 1949. 163 p.
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