Probability and Random Processes

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Geoffrey Grimmett (Director of Research and Professor Emeritus of Mathematical Statistics, Director of Research and Professor Emeritus of Mathematical Statistics, University of Cambridge) David Stirzaker (Professor Emeritus, Professor Emeritus, Mathematical Institute, University of Oxford)

Probability and Random Processes

Geoffrey Grimmett (Director of Research and Professor Emeritus of Mathematical Statistics, Director of Research and Professor Emeritus of Mathematical Statistics, University of Cambridge), David Stirzaker (Professor Emeritus, Professor Emeritus, Mathematical Institute, University of Oxford)

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English

Oxford University Press
01 August 2020

Mathematics & Sciences; Mathematics; Probability & statistics; Stochastics

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.

US BL To provide a thorough but straightforward account of basic probability theory, giving the reader a natural feel for the subject unburdened by oppressive technicalities. BE

BL To discuss important random processes in depth with many examples.BE

BL To cover a range of topics that are significant and interesting but less routine.BE

BL To impart to the beginner some flavour of advanced work.BE UE

OP 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).CP

By: Geoffrey Grimmett (Director of Research and Professor Emeritus of Mathematical Statistics Director of Research and Professor Emeritus of Mathematical Statistics University of Cambridge), David Stirzaker (Professor Emeritus, Professor Emeritus, Mathematical Institute, University of Oxford)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Edition: 4th Revised edition
Dimensions: Height: 253mm, Width: 179mm, Spine: 33mm
Weight: 1g
ISBN: 9780198847601
ISBN 10: 0198847602
Pages: 688
Publication Date: 01 August 2020
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

1: Events and their probabilities 2: Random variables and their distributions 3: Discrete random variables 4: Continuous random variables 5: Generating functions and their applications 6: Markov chains 7: Convergence of random variables 8: Random processes 9: Stationary processes 10: Renewals 11: Queues 12: Martingales 13: Diffusion processes

Geoffrey Grimmett is Professor Emeritus of Mathematical Statistics at the University of Cambridge. Cambridge has been his base for pursuing probability theory and the mathematics of disordered systems since 1992. He was Master of Downing College, Cambridge from 2013-2018 and has been appointed Chair of the Heilbronn Institute for Mathematical Research from 2020. He has written numerous research articles in probability theory and statistical mechanics, as well as three research books. With David Stirzaker and Dominic Welsh respectively, he has co-authored two successful textbooks on probability and random processes at the undergraduate and postgraduate levels. David Stirzaker was educated at Oxford University and Berkeley before being appointed as Fellow and Tutor in Applied Mathematics at St John's College, Oxford. He is now an Emeritus Research Fellow at St John's College, and an Emeritus Professor at the Mathematical Institute, Oxford. He has written five textbooks on probability and random processes, two of them jointly with Geoffrey Grimmett. Most recently, (2015), he has written The Cambridge Dictionary of Probability and its Applications.

Reviews for Probability and Random Processes

Features of PRP include brief but helpful motivational introductions to each subsection, and copious references to historical applications. To aid navigation, definitions, theorems and other key results are highlighted, using three different colours. The tone throughout is rigorous but the touch is human ... * Owen Toller, The Mathematical Gazette * Since its first appearance in 1982 Probability and Random Processes has been a landmark book on the subject and has become mandatory reading for any mathematician wishing to understand chance. It is aimed mainly at final-year honours students and graduate students, but it goes beyond this level, and all serious mathematicians and academic libraries should own a copy ... the companion book of exercises is cleverly conceived and ... forms a perfect complement to the main text. * Times Higher Education Supplement * Review from previous edition...a full and comprehensive account of (almost all) the probability theory and stochastic processes one could hope to teach to undergraduates.... As well as its masterful coverage of the material, the book has many appealing stylistic features ... extremely valuable in finding good proofs of theorems which are dealt with rather cursorily in other textbooks. * The Mathematical Gazette * One of the strong features of the book is its large collection of interesting exercises, which has been greatly expanded in this new edition so that there are now over one thousand. These are conveniently collected together in a separate volume that includes full solutions. * Biometrics *