Article
Licensed
Unlicensed
Requires Authentication
On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands
-
Andrew Rosalsky
Published/Copyright:
February 25, 2010
Abstract
The rate of convergence for an almost surely convergent series of Banach space valued random elements is studied in this paper. As special cases of the main result, known results are obtained for a sequence of independent random elements in a Rademacher type p Banach space, and new results are obtained for a martingale difference sequence of random elements in a martingale type p Banach space and for a p-orthogonal sequence of random elements in a Rademacher type p Banach space. The current work generalizes, simplifies, and unifies some of the recent results of Nam and Rosalsky [Teor. Īmovīr. ta Mat. Statist. 52: 120–131, 1995] and Rosalsky and Rosenblatt [Bull. Inst. Math. Acad. Sinica 11: 185–208, 1983, Nonlinear Anal. 30: 4237–4248, 1997].
Key words and phrases:: Almost surely convergent series of Banach space valued random elements; tail series; rate of convergence; martingale difference sequence; p-orthogonal sequence
Received: 2000-07-03
Published Online: 2010-02-25
Published in Print: 2001-June
© Heldermann Verlag
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Topological Spaces with the Strong Skorokhod Property
- Convergence to Zero and Boundedness of Operator-Normed Sums of Random Vectors with Application to Autoregression Processes
- On a Characterisation of Inner Product Spaces
- On the Tail Estimation of the Norm of Rademacher Sums
- Entropy Numbers of Certain Summation Operators
- Proper Moving Average Representations and Outer Functions in Two Variables
- Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces
- Towards an Innovation Theory of Spatial Brownian Motion under Boundary Conditions
- Entropy Numbers of Diagonal Operators of Logarithmic Type
- On Normal Approximation of Large Products of Functions: A Refinement of Blackwell's Result
- Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators
- Probability Measures with Big Kernels
- Hölder Versions of Banach Space Valued Random Fields
- Representations of Conditional Means
- On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands
- On Stochastic Differential Equations in a Configuration Space
- On Accuracy of Improved χ2-Approximations
- Tractability of Tensor Product Linear Operators in Weighted Hilbert Spaces
Articles in the same Issue
- Topological Spaces with the Strong Skorokhod Property
- Convergence to Zero and Boundedness of Operator-Normed Sums of Random Vectors with Application to Autoregression Processes
- On a Characterisation of Inner Product Spaces
- On the Tail Estimation of the Norm of Rademacher Sums
- Entropy Numbers of Certain Summation Operators
- Proper Moving Average Representations and Outer Functions in Two Variables
- Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces
- Towards an Innovation Theory of Spatial Brownian Motion under Boundary Conditions
- Entropy Numbers of Diagonal Operators of Logarithmic Type
- On Normal Approximation of Large Products of Functions: A Refinement of Blackwell's Result
- Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators
- Probability Measures with Big Kernels
- Hölder Versions of Banach Space Valued Random Fields
- Representations of Conditional Means
- On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands
- On Stochastic Differential Equations in a Configuration Space
- On Accuracy of Improved χ2-Approximations
- Tractability of Tensor Product Linear Operators in Weighted Hilbert Spaces
