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 Ito'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, Levy 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).
Industry Reviews
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 *
