This book presents a selection of topics from probability theory. Essentially, the topics chosen are those that are likely to be the most useful to someone planning to pursue research in the modern theory of stochastic processes. The prospective reader is assumed to have good mathematical maturity. In particular, he should have prior exposure to basic probability theory at the level of, say, K.L. Chung's 'Elementary probability theory with stochastic processes' (Springer-Verlag, 1974) and real and functional analysis at the level of Royden's 'Real analysis' (Macmillan, 1968). The first chapter is a rapid overview of the basics. Each subsequent chapter deals with a separate topic in detail. There is clearly some selection involved and therefore many omissions, but that cannot be helped in a book of this size. The style is deliberately terse to enforce active learning. Thus several tidbits of deduction are left to the reader as labelled exercises in the main text of each chapter. In addition, there are supplementary exercises at the end. In the preface to his classic text on probability ('Probability', Addison Wesley, 1968), Leo Breiman speaks of the right and left hands of probability.
This book is an advanced text on probability theory. By presupposing the
background of a standard first course in real analysis and a 'soft' course
in probability theory, it gives a compact treatment of several key topics
in probability, selected on the basis of their importance in forming the
foundations of the modern theory of stochastic processes. It is ideal for
graduate students and researchers in probability theory and stochastic
processes and their applications. It is also well suited for scientists
in allied fields such as mathematical statistics/ economics/physics, electrical
engineering, operations research who wish to augment their background in
probability theory.
