This text develops the necessary background in probability theory underlying diverse treatments
of stochastic processes and their wide-ranging applications. In this second edition the text
has been reorganized for didactic purposes new exercises have been added and basic theory has
been expanded. General Markov dependent sequences and their convergence to equilibrium is the
subject of an entirely new chapter. The introduction of conditional expectation and conditional
probability very early in the text maintains the pedagogic innovation of the first edition
conditional expectation is illustrated in detail in the context of an expanded treatment of
martingales the Markov property and the strong Markov property. Weak convergence of
probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of
large deviation and or concentration inequalities ranging from those of Chebyshev
Cramer-Chernoff Bahadur-Rao to Hoeffding have been added with illustrative comparisons of
their use in practice. This also includes a treatment of the Berry-Esseen error estimate in the
central limit theorem. The authors assume mathematical maturity at a graduate level otherwise
the book is suitable for students with varying levels of background in analysis and measure
theory. For the reader who needs refreshers theorems from analysis and measure theory used in
the main text are provided in comprehensive appendices along with their proofs for ease of
reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward
Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored
numerous books including a series of four upcoming graduate textbooks in stochastic processes
with applications.
