Mathematics and Its Applications

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 fifty-nine 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 in-depth discussion of modern, highly-specialized 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.

Table of contents (59 chapters)

  • Canonical Equation K 1

    Girko, Vyacheslav L.

    Pages 1-24

  • Canonical Equation K 2. Necessary and Sufficient Modified Lindeberg’s Condition. The Wigner and Cubic Laws

    Girko, Vyacheslav L.

    Pages 25-50

  • Regularized Stochastic Canonical Equation K 3 for Symmetric Random Matrices with Infinitely Small Entries

    Girko, Vyacheslav L.

    Pages 51-74

  • Stochastic Canonical Equation K 4 for Symmetric Random Matrices with Infinitely Small Entries. Necessary and Sufficient Conditions for the Convergence of Normalized Spectral Functions

    Girko, Vyacheslav L.

    Pages 75-86

  • Canonical Equation K 5 for Symmetric Random Matrices with Infinitely Small Entries

    Girko, Vyacheslav L.

    Pages 87-92

Buy this book

eBook $189.00
price for USA (gross)
  • ISBN 978-94-010-0989-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $249.00
price for USA
  • ISBN 978-1-4020-0075-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $249.00
price for USA
  • ISBN 978-94-010-3882-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Theory of Stochastic Canonical Equations
Book Subtitle
Volumes I and II
Authors
Series Title
Mathematics and Its Applications
Series Volume
535
Copyright
2001
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-94-010-0989-8
DOI
10.1007/978-94-010-0989-8
Hardcover ISBN
978-1-4020-0075-1
Softcover ISBN
978-94-010-3882-9
Edition Number
1
Number of Pages
XLVIII, 960
Topics