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 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 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, Levy processes, stability and
self-similarity, time changes, and stochastic calculus including
option pricing via the Black-Scholes model of mathematical finance.
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