The book presents, for the first time, a detailed analysis of harmonizable processes and fields (in the weak sense) that contain the corresponding stationary theory as a subclass. It also gives the structural and some key applications in detail. These include Levy's Brownian motion, a probabilistic proof of the longstanding Riemann's hypothesis, random fields indexed by LCA and hypergroups, extensions to bistochastic operators, Cramér-Karhunen classes, as well as bistochastic operators with some statistical applications.The material is accessible to graduate students in probability and statistics as well as to engineers in theoretical applications. There are numerous extensions and applications pointed out in the book that will inspire readers to delve deeper.

This volume in the series contains chapters on areas such as pareto processes, branching processes, inference in stochastic processes, Poisson approximation, Levy processes, and iterated random maps and some classes of Markov processes. Other chapters cover random walk and fluctuation theory, a semigroup representation and asymptomatic behavior of certain statistics of the Fisher-Wright-Moran coalescent, continuous-time ARMA processes, record sequence and their applications, stochastic networks with product form equilibrium, and stochastic processes in insurance and finance. Other subjects include renewal theory, stochastic processes in reliability, supports of stochastic processes of multiplicity one, Markov chains, diffusion processes, and Ito's stochastic calculus and its applications. c. Book News Inc.

This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochas

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, encouraged by an Air Force Grant for the purpose, and followed by a couple of years more learning opportunity at the Institute for Advanced Study to complete the project. As I progressed, the plan grew larger needing a substantial background material which was made into an independent initial volume in (1979). In its preface I said: "My intension was to present the following material as the first part of a book treating the In ference Theory of stochastic processes, but the latter account has now receded to a distant future," namely for two more decades! Meanwhile, a much enlarged second edition of that early work has appeared (1995), and now I am able to present the main part of the original plan.

"Covers the areas of modern analysis and probability theory. Presents a collection of papers given at the Festschrift held in honor of the 65 birthday of M. M. Rao, whose prolific published research includes the well-received Marcel Dekker, Inc. books Theory of Orlicz Spaces and Conditional Measures and Applications. Features previously unpublished research articles by a host of internationally recognized scholars."

This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.Emphasis is on the use of functional analysis and harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ≥ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.

Most introductory textbooks on stochastic processes which cover standard topics such as Poisson process, Brownian motion, renewal theory and random walks deal inadequately with their applications. Written in a simple and accessible manner, this book addresses that inadequacy and provides guidelines and tools to study the applications. The coverage includes research developments in Markov property, martingales, regenerative phenomena and Tauberian theorems, and covers measure theory at an elementary level.