On the Limit Behavior of Sums of Random Vectors with Values in Hilbert Space

1985 ◽  
Vol 29 (3) ◽  
pp. 620-622 ◽  
Author(s):  
E. R. Vvedenskaya
Keyword(s):  
Hilbert Space ◽  
Limit Behavior ◽  
Random Vectors

scholarly journals Limiting Behavior of the Partial Sum for Negatively Superadditive Dependent Random Vectors in Hilbert Space

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Mi-Hwa Ko
Keyword(s):  
Hilbert Space ◽  
Complete Convergence ◽  
Random Vectors ◽  
Limiting Behavior ◽  
Partial Sum

In this paper, We study the complete convergence and Lp- convergence for the maximum of the partial sum of negatively superadditive dependent random vectors in Hilbert space. The results extend the corresponding ones of Ko (Ko, 2020) to H-valued negatively superadditive dependent random vectors.

Orthogonal Random Vectors and the Hurwitz-Radon-Eckmann Theorem

1994 ◽  
Vol 1 (1) ◽  
pp. 99-113
Author(s):  
N. Vakhania
Keyword(s):  
Hilbert Space ◽  
Nauk Sssr ◽  
Adjoint Operator ◽  
Covariance Operator ◽  
Random Vectors ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
And Topology ◽  
Dimensional Hilbert Space ◽  
Akad Nauk Sssr

Abstract In several different aspects of algebra and topology the following problem is of interest: find the maximal number of unitary antisymmetric operators Ui in with the property UiUj = –UjUi (i ≠ j). The solution of this problem is given by the Hurwitz-Radon-Eckmann formula. We generalize this formula in two directions: all the operators Ui must commute with a given arbitrary self-adjoint operator and H can be infinite-dimensional. Our second main result deals with the conditions for almost sure orthogonality of two random vectors taking values in a finite or infinite-dimensional Hilbert space H. Finally, both results are used to get the formula for the maximal number of pairwise almost surely orthogonal random vectors in H with the same covariance operator and each pair having a linear support in H ⊕ H. The paper is based on the results obtained jointly with N.P.Kandelaki (see [Vakhania and Kandelaki, Dokl. Akad. Nauk SSSR 294: 528-531, 1987, Dokl. Akad. Nauk SSSR 296: 265-266, 1988, Trudy Inst. Vychisl. Mat. Akad. Nauk Gruz. SSR 28: 11-37, 1988]).

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