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Probability and Random Processes
The fourth edition of this successful text provides an introduction to probability and random processes, with many practical applications. It is aimed at mathematics undergraduates and postgraduates, and has four main aims. To provide a thorough but straightforward account of basic probability theory, giving the reader a natural feel for the subject unburdened by oppressive technicalities. To discuss important random processes in depth with many examples. To cover a range of topics that are significant and interesting but less routine. To impart to the beginner some flavour of advanced work.
The book begins with the basic ideas common to most undergraduate courses in mathematics, statistics, and science. It ends with material usually found at graduate level, for example, Markov processes, (including Markov chain Monte Carlo), martingales, queues, diffusions, (including stochastic calculus with Itô's formula), renewals, stationary processes (including the ergodic theorem), and option pricing in mathematical finance using the Black-Scholes formula. Further, in this new revised fourth edition, there are sections on coupling from the past, Lévy processes, self-similarity and stability, time changes, and the holding-time/jump-chain construction of continuous-time Markov chains. Finally, the number of exercises and problems has been increased by around 300 to a total of about 1300, and many of the existing exercises have been refreshed by additional parts. The solutions to these exercises and problems can be found in the companion volume, One Thousand Exercises in Probability, third edition, (OUP 2020).
The book begins with the basic ideas common to most undergraduate courses in mathematics, statistics, and science. It ends with material usually found at graduate level, for example, Markov processes, (including Markov chain Monte Carlo), martingales, queues, diffusions, (including stochastic calculus with Itô's formula), renewals, stationary processes (including the ergodic theorem), and option pricing in mathematical finance using the Black-Scholes formula. Further, in this new revised fourth edition, there are sections on coupling from the past, Lévy processes, self-similarity and stability, time changes, and the holding-time/jump-chain construction of continuous-time Markov chains. Finally, the number of exercises and problems has been increased by around 300 to a total of about 1300, and many of the existing exercises have been refreshed by additional parts. The solutions to these exercises and problems can be found in the companion volume, One Thousand Exercises in Probability, third edition, (OUP 2020).
688 pages, Paperback
First published September 1, 1982
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Displaying 1 - 6 of 6 reviews
March 23, 2008
Our book for MATH 3220 -- Honors Probability and Statistics. While it's just as poorly written as any other undergraduate stochastics book, it's at least got very thorough coverage and a basis in rigorous measure theory. If you're not using measure theory, you're not doing probability, and should slowly back away from the model until you've integrated the Lebesgue into your gestalt.
January 17, 2019
a good book which covers maths of probability and random variable.
I borrowed from the library because I was doing MCMC lab. Unfortunately, it turned out I didn't manage to do a good job because I got too much to (re)learn in two weeks and I was in bad mood. So today's challenge was to finish this book on the train - nice/shamful to see how little I know and how much I have to learn!
I borrowed from the library because I was doing MCMC lab. Unfortunately, it turned out I didn't manage to do a good job because I got too much to (re)learn in two weeks and I was in bad mood. So today's challenge was to finish this book on the train - nice/shamful to see how little I know and how much I have to learn!
February 8, 2020
Very good book but definetly not for beginners. If you want to enjoy reading and studying this one, first consider learning from more introductory books in probability and statistics.
October 8, 2017
Far too difficult as a standard course in undergraduate probability. Some of the exercises have an indulgent/non-instructive feel to them; for example, the very first exercise in section 4.14 is to find \int^{\infty}_{-\infty} e^{-x^2} dx. No hint provided. Seriously? This exercise has no instructive purpose other than to force you to look the answer up if you don't already know the trick.
Instead the breadth of topics and the extensive number of exercises make this book worthwhile for grad students and advanced undergrads. 4 stars (0.5 stars if used as first course in undergrad probability).
Instead the breadth of topics and the extensive number of exercises make this book worthwhile for grad students and advanced undergrads. 4 stars (0.5 stars if used as first course in undergrad probability).
April 24, 2008
the best intro graduate level text i know on probability (and it's not really that great).
December 1, 2015
The content is good, but dense, particularly if it's your first introduction to probability. Should definitely get the companion book containing all the exercises and their solutions.
Displaying 1 - 6 of 6 reviews