Högnäs / Mukherjea Probability Measures on Semigroups

Convolution Products, Random Walks and Random Matrices
2. Auflage 2011
ISBN: 978-0-387-77548-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 430 Seiten

Reihe: Probability and Its Applications

This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices.  In addition, this unique work examines the essentials of abstract semigroup theory and its application to concrete semigroups of matrices.  This substantially revised text includes exercises at various levels at the end of each section and includes the best available proofs on the most important theorems used in a book, making it suitable for a one semester course on semigroups.  In addition, it could also be used as a main text or supplementary material for courses focusing on probability on algebraic structures or weak convergance.  This book is ideally suited to graduate students in mathematics, and students in other fields, such as engineering and the sciences with an interest in probability.  Students in statistics using advanced probability will also find this book useful.

Autoren/Hrsg.

Högnäs, Göran

Mukherjea, Arunava

Inhaltsverzeichnis

1;From the Preface to the First Edition;6
2;Preface to the Second Edition;10
3;Contents;12
4;Chapter 1 Semigroups;14
4.1;1.1 Introduction;14
4.2;1.2 Homomorphisms, Quotients, and Products;19
4.3;1.3 Semigroups with Zero;23
4.4;1.4 The Rees–Suschkewitsch Representation Theorem;25
4.5;1.5 Topological Semigroups;35
4.6;1.6 Semigroups of Matrices;46
4.7;1.7 Semigroups of Infinite Dimensional Matrices;66
4.8;1.8 Notes and Comments;73
5;Chapter 2 Probability Measures on Topological Semigroups;76
5.1;2.1 Introduction;76
5.2;2.2 Invariant and Idempotent Probability Measures;77
5.3;2.3 Weak Convergence of Convolution Products of Probability Measures;96
5.4;2.4 Weak Convergence of Convolution Products of Nonidentical Probability Measures;150
5.5;2.5 Notes and Comments;181
6;Chapter 3 Random Walks on Semigroups;183
6.1;3.1 Introduction;183
6.2;3.2 Discrete Semigroups;192
6.3;3.3 Locally Compact Groups;210
6.4;3.4 Compact Semigroups;231
6.5;3.5 Completely Simple Semigroups;253
6.6;3.6 Notes and Comments;259
7;Chapter 4 Random Matrices;264
7.1;4.1 Introduction;264
7.2;4.2 Recurrent Random Walks in Nonnegative Matrices;265
7.3;4.3 Tightness of Products of I.I.D. Random Matrices: Weak Convergence;295
7.4;4.4 Invariant Measures for Random Walks in Nonnegative Matrices: Laws of Large Numbers;344
7.5;4.5 Notes and Commments;366
8;Appendix A Products of I.I.D. Random Stochastic Matrices: Their Skeletons and Convergence in Distribution;370
9;Appendix B An Example Due to Chamayou and Letac;376
10;Appendix C Asymptotic Behavior of XnXn-1 : : :X0u for I.I.D. Random Nonnegative Matrices;379
11;Appendix D Continuous Singularity of the Limit Distribution of Products of I.I.D. Stochastic Matrices;392
12;Appendix E Rate of Decay of Concentration Functions on Discrete Groups, by T.M. Retzlaff;405
12.1;E.1 Preliminaries;405
12.2;E.2 Irreducible Measures;412
12.3;E.3 Adapted Measures;416
13;References;421
14;Index;431