Theory of Random Determinants
Published on 30. September 1990
Book
Hardback
XXVI, 678 pages
978-0-7923-0233-9 (ISBN)
Description
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.
More details
Series
Edition
1990 ed.
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
XXVI, 678 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 43 mm
Weight
1215 gr
ISBN-13
978-0-7923-0233-9 (9780792302339)
DOI
10.1007/978-94-009-1858-0
Schweitzer Classification
Other editions
Additional editions
Person
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.
Content
1. Generalized Wishart Density and Integral Representation for Determinants.- 2. Moments of Random Matrix Determinants.- 3. Distribution of Eigenvalues and Eigenvectors of Random Matrices.- 4. Inequalities for Random Determinants.- 5. Limit Theorems for the Borel Functions of Independent Random Variables.- 6. Limit Theorems of the Law of Large Numbers and Central Limit Theorem Types for Random Determinants.- 7. Accompanying Infinitely Divisible Laws for Random Determinants.- 8. Integral Representation Method.- 9. The Connection between the Convergence of Random Determinants and the Convergence of Functionals of Random Functions.- 10. Limit Theorems for Random Gram Determinants.- 11. The Determinants of Toeplitz and Hankel Random Matrices.- 12. Limit Theorems for Determinants of Random Jacobi Matrices.- 13. The Fredholm Random Determinants.- 14. The Systems of Linear Algebraic Equations with Random Coefficients.- 15. Limit Theorems for the Solution of the Systems of Linear Algebraic Equations with Random Coefficients.- 16. Integral Equations with Random Degenerate Kernels.- 17. Random Determinants in the Spectral Theory of Non-Self-Adjoint Random Matrices.- 18. The Distribution of Eigenvalues and Eigenvectors of Additive Random Matrix-Valued Processes.- 19. The Stochastic Ljapunov Problem for Systems of Stationary Linear Differential Equations.- 20. Random Determinants in the Theory of Estimation of Parameters of Some Systems.- 21. Random Determinants in Some Problems of Control Theory of Stochastic Systems.- 22. Random Determinants in Some Linear Stochastic Programming Problems.- 23. Random Determinants in General Statistical Analysis.- 24. Estimate of the Solution of the Kolmogorov-Wiener Filter.- 25. Random Determinants in Pattern Recognition.- 26. Random Determinantsin the Experiment Design.- 27. Random Determinants in Physics.- 28. Random Determinants in Numerical Analysis.- References.