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

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### Contents

Introduction | 3 |

Notation and definitions | 19 |

Generalizations of classical channel comparisons | 42 |

Copyright | |

16 other sections not shown

### Common terms and phrases

2-contractive 2-noisier absolutely continuous Ahlswede ak(A apply assume Borel ck(A coefficient of ergodicity column-stochastic matrix columns continuous with respect contraction coefficient convex cone convex function convex hull convex set Corollary Csiszar defined Definition degradation denote denser divergence Dobrushin,s dv(c equivalent essentially strictly convex fixed function f given H^AX H^BX H+(AX H+(X Hellinger distance hence holds I/O-degradation I+(x implies inclusion inequality input symbols Kemperman Lemma less capable Liese and Vajda linear function Lorenz curve lower semicontinuous M+(X Markov kernel measurable spaces Moreover noisier nonnegative O.oo Open Problem p e S2 pair permutation permutation matrix Prob(X probability distribution probability measures Proof Proposition 2.24 Proposition 5.3 prove Remark rows Shannon,s signed measure smaller capacity stable stochastic matrices sublinear function sup sup Suppose supremum Tfi2 Theorem vector