Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics and Population Sciences (Hardcover, 1998)

Part I: Comparing Partial Orderings Among Stochastic Matrices.- Introduction.- Notation and Definitions.- Generalizations of Classical Channel Comparisons.- Degradation is the Same as Increasing Density.- Shannon's Inclusion Implies Smaller Capacity.- A Simple Case: Matrices A and B have only Two Columns.- Open Problems.- Part II: Divergence and Contraction Coefficients.- Introduction, Definitions, and Notation.- A Generalization of an Inequality of Dobrushin.- The Divergence.- Divergence between Images of Measures via Markov Kernels, Contraction Coefficients.- A Particular Case: At Most Countable Spaces.- Behavior of ? ? η_? (T) for a Fixed Markov Kernel T.- Applications of Global Divergence to Comparison of Experiments.- History of the Problem.