Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics and Population

This book generalizes the notion of variation in a set of numbers to variation in a set of probability distributions. It deals with finite stochastic matrices and is presented in an elementary mathematical setting. The introduction, for example, examines applications of concepts and methods in information theory, statistics, economics, and population sciences (population genetics, ecology and demography). Gradually, the exposition becomes more technical, dealing with Markov kernels as generalizations of stochastic matrices.

Stochastic matrices are compared in the context of memoryless channels in information theory; the comparisons are then generalized, and in turn, lead to new implications and results that will add to an array of new concepts and tools for the practitioner.

The overall scope of this work shows important connections among ideas from diverse fields including mathematics, economics, and biology. Its clarity of presentation makes this a resource or a good for self-study or for graduate course.