This book is a photographic reproduction of the book of the same title published in 1981, for which there has been continuing demand on account of its accessible technical level. Its appearance also helped generate considerable subsequent work on inhomogeneous products of matrices. This printing adds an additional bibliography on coefficients of ergodicity and a list of corrigenda. Eugene Seneta received his Ph.D. in 1968 from the Australian National University. He left Canberra in 1979 to become Professor and Head of the Department of Mathematical Statistics at the University of Sydney. He has been a regular visitor to the United States, most frequently to the University of Virginia. Now Emeritus Professor at the University of Sydney, he has recently developed a renewed interest in financial mathematics. He was elected Fellow of the Australian Academy of Science in 1985 and awarded the Pitman Medal of the Statistical Society of Australia for his distinguished research contributions. The first edition of this book, entitled Non-Negative Matrices, appeared in 1973, and was followed in 1976 by his Regularly Varying Functions in the Springer Lecture Notes in Mathematics, later translated into Russian. Both books were pioneering in their fields. In 1977, Eugene Seneta coauthored (with C. C. Heyde ) I.J. Bienaymé : Statistical Theory Anticipated, which is effectively a history of probability and statistics in the 19th century, and in 2001 co-edited with the same colleague Statisticians of the Centuries, both published by Springer. Having served on the editorial board of the Encyclopedia of Statistical Science, he is currently Joint Editor of the International Statistical Review.
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This book is a photographic reproduction of the book of the same title published in 1981, for which there has been continuing demand on account of its accessible technical level. Its appearance also helped generate considerable subsequent work on inhomogeneous products of matrices. This printing adds an additional bibliography on coefficients of ergodicity and a list of corrigenda. Eugene Seneta received his Ph.D. in 1968 from the Australian National University. He left Canberra in 1979 to become Professor and Head of the Department of Mathematical Statistics at the University of Sydney. He has been a regular visitor to the United States, most frequently to the University of Virginia. Now Emeritus Professor at the University of Sydney, he has recently developed a renewed interest in financial mathematics. He was elected Fellow of the Australian Academy of Science in 1985 and awarded the Pitman Medal of the Statistical Society of Australia for his distinguished research contributions. The first edition of this book, entitled Non-Negative Matrices, appeared in 1973, and was followed in 1976 by his Regularly Varying Functions in the Springer Lecture Notes in Mathematics, later translated into Russian. Both books were pioneering in their fields. In 1977, Eugene Seneta coauthored (with C. C. Heyde ) I.J. Bienaymé : Statistical Theory Anticipated, which is effectively a history of probability and statistics in the 19th century, and in 2001 co-edited with the same colleague Statisticians of the Centuries, both published by Springer. Having served on the editorial board of the Encyclopedia of Statistical Science, he is currently Joint Editor of the International Statistical Review.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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irreducible matrices, marginal totals, single essential class, ergodicity obtains, elementwise finite, superregular vector, northwest corner truncation, finite stochastic matrices, subinvariant vector, common convergence radius, inessential indices, unique stationary distribution vector, subinvariant measure, asymptotic homogeneity, inhomogeneous products, strong ergodicity, same incidence matrix, weak ergodicity, scrambling matrix, inessential classes, backwards products, cofactor properties, inessential states, projective distance, backward products Key Phrases - Capitalized Phrases (CAPs): (learn more)
Some Secondary Theory, Countable Stochastic Matrices, Inhomogeneous Products of Non-negative Matrices, Birkhoff's Contraction Coefficient, Perron-Frobenius Theorem, Truncations of Infinite Stochastic Matrices, Basic Assumption, Fatou's Lemma, Finite Homogeneous Markov Chains, Estimating Non-negative Matrices, Theory of Non-negative Matrices, The Equations, Derivation of Explicit Form, General Non-negative Matrix, Countable Non-negative Matrices, Some Extensions of the Perron-Frobenius Structure, Classification of Indices, Quasi-stationary Distributions, The Probability Algorithm, Irreducible Stochastic Matrices, Finite Approximations Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
irreducible matrices, marginal totals, single essential class, ergodicity obtains, elementwise finite, superregular vector, northwest corner truncation, finite stochastic matrices, subinvariant vector, common convergence radius, inessential indices, unique stationary distribution vector, subinvariant measure, asymptotic homogeneity, inhomogeneous products, strong ergodicity, same incidence matrix, weak ergodicity, scrambling matrix, inessential classes, backwards products, cofactor properties, inessential states, projective distance, backward products Key Phrases - Capitalized Phrases (CAPs): (learn more)
Some Secondary Theory, Countable Stochastic Matrices, Inhomogeneous Products of Non-negative Matrices, Birkhoff's Contraction Coefficient, Perron-Frobenius Theorem, Truncations of Infinite Stochastic Matrices, Basic Assumption, Fatou's Lemma, Finite Homogeneous Markov Chains, Estimating Non-negative Matrices, Theory of Non-negative Matrices, The Equations, Derivation of Explicit Form, General Non-negative Matrix, Countable Non-negative Matrices, Some Extensions of the Perron-Frobenius Structure, Classification of Indices, Quasi-stationary Distributions, The Probability Algorithm, Irreducible Stochastic Matrices, Finite Approximations Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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42
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cite this book:
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- Numerical Solution of Markov Chains (Probability: Pure and Applied) by William J. Stewart on page 129, page 528, and page 640
- Fitting Linear Relationships: A History of the Calculus of Observations 1750-1900 (Springer Series in Statistics) by R.W. Farebrother in Back Matter (1), and Back Matter (2)
- Analysis of Variance for Random Models, Volume 2: Unbalanced Data: Theory, Methods, Applications, and Data Analysis by Hardeo Sahai on page 11, and Back Matter
- Artificial Immune Systems: 4th International Conference, ICARIS 2005, Banff, Alberta, Canada, August 14-17, 2005, Proceedings (Lecture Notes in ... Computer Science and General Issues) by Christian Jacob on page 330
- STOCHASTIC MODELS HORM2, Volume 2 (Handbooks in Operations Research and Management Science) by D.P. Heyman on page 433
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