Probability and Random Processes with One Thousand Exercises in Probability

ISBN-13: 9780198847625 / Angielski / Miękka / 2020 / 1168 str.

Geoffrey Grimmett; David Stirzaker

Opis

Probability and Random Processes 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 financeusing 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 hasbeen increased by around 300 to a total of about 1317, 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.One Thousand Exercises in Probability, third edition is a revised, updated, and greatly expanded version of previous edition of 2001. The 1300+ exercises contained within are not merely drill problems, but have been chosen to illustrate the concepts, illuminate the subject, and both inform and entertain the reader. A broad range of subjects is covered, including elementary aspects of probability and random variables, sampling, generating functions, Markov chains, convergence,stationary processes, renewals, queues, martingales, diffusions, Lévy processes, stability and self-similarity, time changes, and stochastic calculus including option pricing via the Black-Scholes model of mathematical finance.

The fourth edition of Probability and Random Processes provides an introduction to probability and random processes, with many practical applications, together with the third edition of One Thousand Exercises in Probability; revised, updated, and greatly expanded version of previous edition of 2001.

O autorze

Geoffrey Grimmett was educated at Oxford University before moving in 1976 to Bristol University for his first tenured post. After sixteen wonderful years in Bristol, he moved in 1992 to the Statistical Laboratory of Cambridge University as Professor of Mathematical Statistics. Cambridge remains his base for pursuing probability theory and the mathematics of disordered systems. He was Master of Downing College, Cambridge from 2013-2018 and has been appointed Chair of the Heilbronn Institute for Mathematical Research from 2020. 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.