Artikel
Lizenziert
Nicht lizenziert
Erfordert eine Authentifizierung
CLT for Operator Abel Sums of Random Elements
-
Tengiz Shervashidze
Veröffentlicht/Copyright:
11. März 2010
Abstract
Let (ξ𝑘)𝑘 ≥ 1 be a sequence of independent, identically distributed second order mean zero random elements in a separable Hilbert space 𝐻 and 𝐴 be an element of a certain class of linear continuous operators 𝐻 → 𝐻 such that ‖𝐴‖ < 1. Denote 
. We prove that if ‖𝐼 – 𝐴‖ tends to zero, where 𝐼 is the identity operator, then the normalized sum (𝐼 – 𝐴2)1/2η𝐴 converges in distribution to a Gaussian random element.
Received: 2008-03-21
Published Online: 2010-03-11
Published in Print: 2008-December
© Heldermann Verlag
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Artikel in diesem Heft
- On Iterative Combination of Modified Bernstein-Type Polynomials
- On Dynamical Three-Dimensional Fluid-Solid Interaction Problem
- Existence and Uniqueness of Weak Solution for a Class of Elliptic Reaction-Diffusion Systems
- Existence of Solutions in Weighted Sobolev Spaces for Some Degenerate Quasilinear Elliptic Equations
- Periodic Solutions for Nonlinear Differential Equation with Functional Delay
- Restriction Theorems for Anisotropically Homogeneous Hypersurfaces of
- Dual Variational Method for a Fourth Order Dirichlet Problem
- On Some Combinatorial Problems Concerning Geometrical Realizations of Finite and Infinite Families of Sets
- Beurling–Borg Type Theorem for Two-Dimensional Linear Differential Systems
- The Maximal Operator in Weighted Variable Exponent Spaces on Metric Spaces
- Sequential Detection of Drift Change for Brownian Motion with Unknown Sign
- Uniqueness for Meromorphic Functions Concerning Differential Polynomials
- Integral Representations and Continuous Projectors in Some Spaces of Analytic and Pluriharmonic Functions
- On One Problem with the Condition at Infinity for Second Order Singular Ordinary Differential Equations
- Rectifiable and Unrectifiable Oscillations for a Generalization of the Riemann–Weber Version of Euler Differential Equation
- Compact Composition Operators on Generalized Hardy Spaces
- CLT for Operator Abel Sums of Random Elements
- On the Dirichlet Problem for a Second Order Elliptic System with Degeneration on the Whole Boundary of a Multidimensional Domain
- A Note on Conjugacy Classes of Finite Groups
Artikel in diesem Heft
- On Iterative Combination of Modified Bernstein-Type Polynomials
- On Dynamical Three-Dimensional Fluid-Solid Interaction Problem
- Existence and Uniqueness of Weak Solution for a Class of Elliptic Reaction-Diffusion Systems
- Existence of Solutions in Weighted Sobolev Spaces for Some Degenerate Quasilinear Elliptic Equations
- Periodic Solutions for Nonlinear Differential Equation with Functional Delay
- Restriction Theorems for Anisotropically Homogeneous Hypersurfaces of
- Dual Variational Method for a Fourth Order Dirichlet Problem
- On Some Combinatorial Problems Concerning Geometrical Realizations of Finite and Infinite Families of Sets
- Beurling–Borg Type Theorem for Two-Dimensional Linear Differential Systems
- The Maximal Operator in Weighted Variable Exponent Spaces on Metric Spaces
- Sequential Detection of Drift Change for Brownian Motion with Unknown Sign
- Uniqueness for Meromorphic Functions Concerning Differential Polynomials
- Integral Representations and Continuous Projectors in Some Spaces of Analytic and Pluriharmonic Functions
- On One Problem with the Condition at Infinity for Second Order Singular Ordinary Differential Equations
- Rectifiable and Unrectifiable Oscillations for a Generalization of the Riemann–Weber Version of Euler Differential Equation
- Compact Composition Operators on Generalized Hardy Spaces
- CLT for Operator Abel Sums of Random Elements
- On the Dirichlet Problem for a Second Order Elliptic System with Degeneration on the Whole Boundary of a Multidimensional Domain
- A Note on Conjugacy Classes of Finite Groups
