A generalization of Chebyshev’s inequality for Hilbert-space-valued random elements

2014 ◽  
Vol 88 ◽  
pp. 62-65 ◽  
Author(s):  
Katarzyna Budny
Keyword(s):  
Hilbert Space ◽  
Chebyshev’S Inequality ◽  
Random Elements ◽  
Chebyshev's Inequality

Chebyshev’s Inequality-Based Multisensor Data Fusion in Self-Organizing Sensor Networks

2016 ◽  
pp. 553-567
Author(s):  
Mengxia Zhu ◽  
Richard R. Brooks ◽  
Song Ding ◽  
Qishi Wu ◽  
Nageswara S.V. Rao ◽  
...  
Keyword(s):  
Sensor Networks ◽  
Data Fusion ◽  
Chebyshev’S Inequality ◽  
Multisensor Data Fusion ◽  
Chebyshev's Inequality ◽  
Multisensor Data ◽  
Self Organizing

Asymptotic normality of sums of Hilbert space valued random elements

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Alfredas Račkauskas
Keyword(s):  
Hilbert Space ◽  
Asymptotic Normality ◽  
Separable Hilbert Space ◽  
Linear Process ◽  
Weighted Sums ◽  
Bounded Operators ◽  
Linear Processes ◽  
Summation Methods ◽  
Random Elements

Abstract We investigate the asymptotic normality of distributions of the sequence {\sum_{k\in\mathbb{Z}}u_{n,k}X_{k}} , {n\in\mathbb{N}} , where {(X_{k},k\in\mathbb{Z})} either is a sequence of i.i.d. random elements or constitutes a linear process with i.i.d. innovations in a separable Hilbert space. The weights {(u_{n,k})} are in general a family of linear bounded operators. This model includes operator weighted sums of Hilbert space valued linear processes, operator-wise discounted sums in a Hilbert space as well some extensions of classical summation methods.

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