Probability and Random Processes

This third edition of this successful text gives a rigorous and extensive introduction to probability theory and an account in some depth of the most important random processes. It includes various topics which are suitable for undergraduate courses, but are not routinely taught.It is suitable for students of probability at all levels. There are four main aims: 1) to provide a thorough but straightforward account of basic probability, giving the reader a natural feel for the subject unburdened by oppressive technicalities, 2) to discuss important random processes in depth with many examples. 3) to cover a range of important but less routine topics, 4) to impart to the beginner the flavour of more advanced work.The book begins with basic ideas common to many undergraduate courses in mathematics, statistics and the sciences; it concludes with topics usually found at graduate level. The ordering and numbering of material in this third edition has been mostly preserved from the second. Minor alterations and additions have been added for clearer exposition. Highlights include new sections on sampling and Markov chain Monte Carlo, geometric probability, coupling and Poisson approximation, large deviations, spatial Poisson processes, renewal-reward, queuing networks, stochastic calculus, Ito's formula and option pricing in the Black- Scholes model for financial markets.In addition there are many (nearly 400) new exercises and problems that are entertaining and instructive; their solutions can be found in the companion volume 'One Thousand Exercises in Probability', (OUP). This completely revised text provides a simple but rigorous introduction to probability. It discusses a wide range of random processes in some depth with many examples, and gives the beginner some flavor of more advanced work, by suitable choice of material. The book begins with basic material commonly covered in first-year undergraduate mathematics and statistics courses, and finishes with topics found in graduate courses. Important features of this edition include new and expanded sections in the early chapters, providing more illustrative examples and introducing more ideas early on; two new chapters providing more comprehensive treatment of the simpler properties of martingales and diffusion processes; and more exercises at the ends of almost all sections, with many new problems at the ends of chapters. This textbook provides a wide-ranging and entertaining indroduction to probability and random processes and many of their practical applications. It includes many exercises and problems with solutions The volume will be useful to all those teachers of probability and random processes who set work assignments and examinations.