Non-negative Matrices and Markov Chains / Edition 2

by E. Seneta

Overview

Since its inception by Perron and Frobenius, the theory of non-negative matrices has developed enormously and is now being used and extended in applied fields of study as diverse as probability theory, numerical analysis, demography, mathematical economics, and dynamic programming, while its development is still proceeding rapidly as a branch of pure mathematics in its own right. While there are books which cover this or that aspect of the theory, it is nevertheless not uncommon for workers in one or another branch of its development to be unaware of what is known in other branches, even though there is often formal overlap. One of the purposes of this book is to relate several aspects of the theory, insofar as this is possible. The author hopes that the book will be useful to mathematicians; but in particular to the workers in applied fields, so the mathematics has been kept as simple as could be managed. The mathematical requisites for reading it are: some knowledge of real-variable theory, and matrix theory; and a little knowledge of complex-variable; the emphasis is on real-variable methods. (There is only one part of the book, the second part of 55.5, which is of rather specialist interest, and requires deeper knowledge.) Appendices provide brief expositions of those areas of mathematics needed which may be less g- erally known to the average reader.

Product Details

ISBN-13:	9780387297651
Publisher:	Springer New York
Publication date:	01/26/2006
Series:	Springer Series in Statistics
Edition description:	Softcover reprint of the original 2nd ed. 1981
Pages:	281
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Finite Non-Negative Matrices.- Fundamental Concepts and Results in the Theory of Non-negative Matrices.- Some Secondary Theory with Emphasis on Irreducible Matrices, and Applications.- Inhomogeneous Products of Non-negative Matrices.- Markov Chains and Finite Shastic Matrices.- Countable Non-Negative Matrices.- Countable Shastic Matrices.- Countable Non-negative Matrices.- Truncations of Infinite Shastic Matrices.