This is a revised and expanded edition of a successful graduate and reference text. The book is designed for a standard graduate course on probability theory, including some important applications. The new edition offers a detailed treatment of the core area of probability, and both structural and limit results are presented in detail. Compared to the first edition, the material and presentation are better highlighted; each chapter is improved and updated.

The material accumulated and presented in this volume can be ex plained easily. At the start of my graduate studies in the early 1950s, I Grenander's (1950) thesis, and was much attracted to the came across entire subject considered there. I then began preparing for the neces sary mathematics to appreciate and possibly make some contributions to the area. Thus after a decade of learning and some publications on the way, I wanted to write a modest monograph complementing Grenander's fundamental memoir. So I took a sabbatical leave from my teaching position at the Carnegie-Mellon University,...

Like many other textbooks aimed at an advanced graduate audience, Rao's (math, U. of California-Riverside) can also be used as a reference by working professionals. Rao exerts himself considerably to prevent these two uses from conflicting by frequently restating key concepts, keeping the chapters r

The second edition of this authoritative text offers an in-depth treatment of all aspects of conditional expectations and probability measures and their structural analysis. However, what makes this the definitive reference on conditional measures is the author's keen ability to link theory with practical applications. The author covers applications in sufficiency, Markov processes and martingales. He also illustrates the difficulties in calculating conditional expectations for continuous multivariate distributions and methods for correct solutions in such cases. Each chapter concludes with...

Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail....