Theory of Random Determinants

1. Front Matter

   Pages i-xxv

   PDF

2. Generalized Wishart Density and Integral Representation for Determinants

   • V. L. Girko

   Pages 1-21

3. Moments of Random Matrix Determinants

   • V. L. Girko

   Pages 22-53

4. Distribution of Eigenvalues and Eigenvectors of Random Matrices

   • V. L. Girko

   Pages 54-101

5. Inequalities for Random Determinants

   • V. L. Girko

   Pages 102-113

6. Limit Theorems for the Borel Functions of Independent Random Variables

   • V. L. Girko

   Pages 114-169

7. Limit Theorems of the Law of Large Numbers and Central Limit Theorem Types for Random Determinants

   • V. L. Girko

   Pages 170-203

8. Accompanying Infinitely Divisible Laws for Random Determinants

   • V. L. Girko

   Pages 204-217

9. Integral Representation Method

   • V. L. Girko

   Pages 218-254

10. The Connection Between the Convergence of Random Determinants and the Convergence of Functionals of Random Functions

    • V. L. Girko

    Pages 255-296

11. Limit Theorems for Random Gram Determinants

    • V. L. Girko

    Pages 297-308

12. The Determinants of Toeplitz and Hankel Random Matrices

    • V. L. Girko

    Pages 309-320

13. Limit Theorems for Determinants of Random Jacobi Matrices

    • V. L. Girko

    Pages 321-346

14. The Fredholm Random Determinants

    • V. L. Girko

    Pages 347-365

15. The Systems of Linear Algebraic Equations with Random Coefficients

    • V. L. Girko

    Pages 366-376

16. Limit Theorems for the Solution of the Systems of Linear Algebraic Equations with Random Coefficients

    • V. L. Girko

    Pages 377-390

17. Integral Equations with Random Degenerate Kernels

    • V. L. Girko

    Pages 391-400

18. Random Determinants in the Spectral Theory of Non-Self-Adjoint Random Matrices

    • V. L. Girko

    Pages 401-441

19. The Distribution of Eigenvalues and Eigenvectors of Additive Random Matrix-Valued Processes

    • V. L. Girko

    Pages 442-467

20. The Stochastic Ljapunov Problem for Systems of Stationary Linear Differential Equations

    • V. L. Girko

    Pages 468-480

• Covariance matrix
• Kolmogorov equations
• Law of large numbers
• Markov chain
• Martingale
• Normal distribution
• Optimal control
• Random variable
• Sturm-Liouville problem
• Variance
• calculus
• differential equation
• random function
• random walk
• statistics

• Dapartment of Cybernetics, Kiev State University, USSR

  V. L. Girko

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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