Overview
- Presents up-to-date material
- Examines abstract semigroup theory and its application to concrete semigroups of matrices
- Includes exercises at various levels
- Includes the best available proofs on the most important theorems used in a book
Part of the book series: Probability and Its Applications (PIA)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
From the reviews of the second edition:
`A well-written book...This is elegant mathematics, motivated by examples and presented in an accessible way that engages the reader.'
International Statistics Institute, December 1996
`This beautiful book...guides the reader through the most important developments...a valuable addition to the library of the probabilist, and a must for anybody interested in probability on algebraic structures.'
Zentralblatt für Mathematik und ihre Grenzgebiete-Mathematical Abstracts
`This well-written volume, by two of the most successful workers in the field....deserves to become the standard introduction for beginning researchers in this field.'
Journal Royal Statistical Society
“Högnäs and Mukherjea have made substantial contributions to the subject themselves and present their work and that of others in a unified way. … For students … this book is an excellent account of the long-term behavior of random transformations. It organizes the ideas very well and its development of the theory is clear and rigorous. … a useful reference for anyone interested in random walks on semigroups and groups. … will be valuable to any reader who wishes to learn the subject … .” (George Willis, SIAM Review, Vol. 54 (2), 2012)
Authors and Affiliations
Bibliographic Information
Book Title: Probability Measures on Semigroups
Book Subtitle: Convolution Products, Random Walks and Random Matrices
Authors: Göran Högnäs, Arunava Mukherjea
Series Title: Probability and Its Applications
DOI: https://doi.org/10.1007/978-0-387-77548-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Hardcover ISBN: 978-0-387-77547-0Published: 10 November 2010
Softcover ISBN: 978-1-4614-2732-2Published: 25 December 2012
eBook ISBN: 978-0-387-77548-7Published: 02 November 2010
Series ISSN: 1431-7028
Edition Number: 2
Number of Pages: XII, 430
Topics: Probability Theory and Stochastic Processes, Probability and Statistics in Computer Science, Topological Groups, Lie Groups, Analysis