Probability Measures on Semigroups (eBook)

Convolution Products, Random Walks and Random Matrices

Göran Högnäs, Arunava Mukherjea (Autoren)

eBook Download: PDF

2010 | 2nd ed. 2011
XII, 430 Seiten
Springer US (Verlag)
978-0-387-77548-7 (ISBN)

Infos

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.

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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 convergence.  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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 2.11.2010
• Reihe/Serie: Probability and Its Applications
• Reihe/Serie: Probability and Its Applications
• Zusatzinfo: XII, 430 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• ISBN-10: 0-387-77548-X / 038777548X
• ISBN-13: 978-0-387-77548-7 / 9780387775487