Theory of Stochastic Canonical Equations
Volumes I and II
Authors: Girko, V.L.
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 About this book

Theory of Stochastic Canonical Equations collects the major results of thirty years of the author's work in the creation of the theory of stochastic canonical equations. It is the first book to completely explore this theory and to provide the necessary tools for dealing with these equations. Included are limit phenomena of sequences of random matrices and the asymptotic properties of the eigenvalues of such matrices. The book is especially interesting since it gives readers a chance to study proofs written by the mathematician who discovered them.
All fiftynine canonical equations are derived and explored along with their applications in such diverse fields as probability and statistics, economics and finance, statistical physics, quantum mechanics, control theory, cryptography, and communications networks. Some of these equations were first published in Russian in 1988 in the book Spectral Theory of Random Matrices, published by Nauka Science, Moscow.
An understanding of the structure of random eigenvalues and eigenvectors is central to random matrices and their applications. Random matrix analysis uses a broad spectrum of other parts of mathematics, linear algebra, geometry, analysis, statistical physics, combinatories, and so forth. In return, random matrix theory is one of the chief tools of modern statistics, to the extent that at times the interface between matrix analysis and statistics is notably blurred.
Volume I of Theory of Stochastic Canonical Equations discusses the key canonical equations in advanced random matrix analysis. Volume II turns its attention to a broad discussion of some concrete examples of matrices. It contains indepth discussion of modern, highlyspecialized topics in matrix analysis, such as unitary random matrices and Jacoby random matrices.
The book is intended for a variety of readers: students, engineers, statisticians, economists and others.  About the authors

Vyacheslav L. Girko is Professor of Mathematics in the Department of Applied Statistics at the National University of Kiev and the University of Kiev Mohyla Academy. He is also affiliated with the Institute of Mathematics, Ukrainian Academy of Sciences. His research interests include multivariate statistical analysis, discriminant analysis, experiment planning, identification and control of complex systems, statistical methods in physics, noise filtration, matrix analysis, and stochastic optimization. He has published widely in the areas of multidimensional statistical analysis and theory of random matrices.
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Bibliographic Information
 Bibliographic Information

 Book Title
 Theory of Stochastic Canonical Equations
 Book Subtitle
 Volumes I and II
 Authors

 V.L. Girko
 Series Title
 Mathematics and Its Applications
 Series Volume
 535
 Copyright
 2001
 Publisher
 Springer Netherlands
 Copyright Holder
 Springer Science+Business Media New York
 eBook ISBN
 9789401009898
 DOI
 10.1007/9789401009898
 Hardcover ISBN
 9781402000751
 Softcover ISBN
 9789401038829
 Edition Number
 1
 Number of Pages
 XLVIII, 960
 Topics