Books in the Probability and Its Applications series

This book offers a detailed review of perturbed random walks, perpetuities, and random processes with immigration.

The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book.

This book presents basic properties of self-similar processes, focusing on the study of their variation using stochastic analysis, and also surveys recent techniques and findings on limit theorems and Malliavin calculus.

This volume covers recent developments in self-normalized processes, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales.

This book unifies much research scattered in the literature, and introduces new results first proved by the author. Also presents practical applications, in such highly interesting areas as approximation theory, cosmology and earthquake engineering.

This book presents mathematical techniques for understanding sequence evolution. The theory is developed in close connection with data from more than 60 experimental studies that illustrate the use of these results.

Three centuries ago Montmort and De Moivre published two books on probability theory emphasizing its most important application at that time, games of chance. This book, on the probabilistic aspects of gambling, is a modern version of those classics.

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology. This volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction.

Fully revised and updated by the authors who have reworked their 1988 first edition, this brilliant book brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition.

Mass transportation problems concern the optimal transfer of masses from one location to another. This title is suitable for researchers in applied probability, operations research, computer science, and mathematical economics.

Randomly Stopped Processes U-Statistics and Processes Martingales and Beyond

The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches.

Mass transportation problems concern the optimal transfer of masses from one location to another. This first of two volumes is a useful reference for researchers in applied probability, operations research, computer science, and mathematical economics.

Applications vary from classical probability estimates to modern extreme value theory and combinatorial counting to random subset selection. Applications are given in prime number theory, growth of digits in different algorithms, and in statistics such as estimates of confidence levels of simultaneous interval estimation.

The first and only book to make this research available in the West Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist Each chapter is self-contained to make the book easy-to-use

The Malliavin calculus is an infinite-dimensional differential calculus on a Gaussian space, developed to provide a probabilistic proof to Hoermander's sum of squares theorem but has found a range of applications in stochastic analysis.

This book gives a self-contained introduction to the dynamic martingale approach to marked point processes (MPP).