Products of Random Variables explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and number theory. It uses entirely probabilistic arguments in actualizing the potential of the asymptotic theory of products of independent random variables and obtaining results with dependent variables using a new Bonferroni-type argument.
Systematically and comprehensively tracks the progression of research completed in the area over the last twenty years.
Well-indexed and well-referenced, Products of Random Variables
Clarifies foundational concepts such as symmetric and limiting distributions of products
Examines various limit theorems, from logarithmically Poisson distributions to triangular arrays
Explores characterization theorems, detailing normal, Cauchy, and bivariate distributions
Describes models of interactive particles
Elucidates dual systems of interactive particles, dual systems of increasing size, and random walks
Covers the Kubilius-Turán inequality and distributions for multiplicative functions
Probes sequences of prime divisors and prime numbers
Discusses Markov chains, Hilbert spaces, and quotients of random variables
Presents income growth models and numerous other applied models tapping products of random variables
Authored by eminent scholars in the field, this volume is an important research reference for applied mathematicians, statisticians, physicists, and graduate students in these disciplines.
Table of Contents
"This book is the first monograph that is completely devoted to the theory of products of random variables (PRV). It gives the most comprehensive review of the recent results in this area and could be used as a handbook in PRV…the subject index covers the content of the book quite satisfactorily. This book is a useful source of information for specialists in probability theory and/or number theory. This volume will be very useful in any mathematical library."
-Mathematical Reviews, Issue 2005g