Probability and measure. 2nd ed. (English) Zbl 0649.60001

Billingsley, Patrick

Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. New York etc.: John Wiley & Sons, Inc. XIV, 622 p.; $ 44.95 (1986).

[For the review of the first edition from 1979 see Zbl 0411.60001.]
In addition to correcting some errors, we have in this edition expanded the treatment of several topics, such as the asymptotic behavior of Markov chains, and added a few new ones, such as a central limit theorem for martingales. Although we have made cuts here and there, the second edition is longer than the first. It is still possible to cover most of the book in one academic year if all the starred topics are omitted.

MSC:

60-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60Bxx	Probability theory on algebraic and topological structures
28Axx	Classical measure theory
60Fxx	Limit theorems in probability theory
60E07	Infinitely divisible distributions; stable distributions
60E10	Characteristic functions; other transforms
60G50	Sums of independent random variables; random walks
60J05	Discrete-time Markov processes on general state spaces
60K25	Queueing theory (aspects of probability theory)

Keywords:

iterated logarithm; Markov chains; moment generating functions; sum of independent random variables; queues; random walk; weak convergence; central limit theorem

Citations:

Zbl 0172.212; Zbl 0411.60001