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 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).CP
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