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

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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.