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Probability and random processes / G. R. Grimmett and D. R. Stirzaker

Auteur principal : Grimmett, Geoffrey R., 1950-, AuteurCo-auteur : Stirzaker, David R., 1947-, AuteurType de document : MonographieLangue : anglais.Pays : Etats Unis.Mention d'édition: 2nd ed.Éditeur : New York : Oxford University Press, 1995Description : 1 vol. (XII-541 p.) : graph. ; 24 cmISBN : 0198536658.Bibliographie : Bibliogr. p. [532]-533. Index.Sujet MSC : 60-01, Probability theory and stochastic processes, Instructional exposition (textbooks, tutorial papers, etc.)
60Gxx, Probability theory and stochastic processes, Stochastic processes
60Jxx, Probability theory and stochastic processes, Markov processes
60Kxx, Probability theory and stochastic processes, Special processes
En-ligne : Zentralblatt | MathSciNet
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60 GRI (Browse shelf) Available 11541-01

This textbook starts from the elements of probability, such as events and random variables, and moves on to more advanced topics such as discrete Markov chains in discrete time, discrete Markov processes in continuous time, stationary processes, spectral representation, the ergodic theorem, renewal theory and martingales. Also a number of special processes like birth-death processes, branching processes, queues and diffusion are treated in some detail. The authors describe the book as undergraduate (and a reference for graduates), but presumably it is more at the graduate level. In fact, it is remarkable how many of the main basic topics of probability theory are given a rather complete introduction. Conditional expectations given σ-fields are used, but otherwise, the level of measure theory is very moderate. There is a great number of exercises and problems to each chapter. This number has been expanded in the second edition, and as a further novelty, a solution manual accompanies the book. Also special processes and martingales are given more attention compared to the first edition, and some modern ideas have entered, e.g. coupling as a tool for proving limit theorems for Markov chains. (Zentralblatt)

Bibliogr. p. [532]-533. Index

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