Self averaging of normalized spectral functions of some product of independent random matrices of growing dimension
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A. I. Vladimirova
The problem of the spectral analysis of random matrizant (the product of random matrices), which is the solution of a recurrent system of equations with random coefficients, or the system of stochastic linear differential equations of growing dimension is considered. The growing dimension means that the dimension of matrices and the number of matrices have the same order and both (dimension and number of matrices) tend to infinity. In this paper we give new method of deriving self averaging property for the V.I.C.T.O.R.I.A.-transform of normalized spectral functions (n.s.f.) of random matrizant or the product of independent random matrices. We apply the REFORM method for normalized spectral functions of this matrizant, where random matrices belong to the domain of attraction of the Strong Circular Law.
© de Gruyter 2007
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- Approximation of random dynamical systems with discrete time by stochastic differential equations: I. Theory
- Two-boundary problems for semi-Markov walk with a linear drift
- Self averaging of normalized spectral functions of some product of independent random matrices of growing dimension
- Weak solutions and a Yamada–Watanabe theorem for FBSDEs
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Artikel in diesem Heft
- Approximation of random dynamical systems with discrete time by stochastic differential equations: I. Theory
- Two-boundary problems for semi-Markov walk with a linear drift
- Self averaging of normalized spectral functions of some product of independent random matrices of growing dimension
- Weak solutions and a Yamada–Watanabe theorem for FBSDEs
- M-estimates for stationary and scaled residuals
- A simple formula for parabolic cylinder functions
- Correction on a generalized BSDE involving local time and application to a PDE with nonlinear boundary condition
