Complete Moment Convergence for Sung’s Type Weighted Sums of B -Valued Random Elements
Joint Authors
Sung, Soo Hak
Li, Wei
Chen, Pingyan
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-03-30
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Let p ≥ 1 / α and 1 / 2 < α ≤ 1 .
Let { X , X n , n ≥ 1 } be a sequence of independent and identically distributed B -valued random elements and let { a n i , 1 ≤ i ≤ n , n ≥ 1 } be an array of real numbers satisfying ∑ i = 1 n a n i q = O ( n ) for some q > p .
We give necessary and sufficient conditions for complete moment convergence of the form ∑ n = 1 ∞ n ( p - v ) α - 2 E ∑ i = 1 n a n i X i - ε n α + v < ∞ , ∀ ε > 0 , where 0 < v < p .
A strong law of large numbers for weighted sums of independent B -valued random elements is also obtained.
American Psychological Association (APA)
Li, Wei& Chen, Pingyan& Sung, Soo Hak. 2016. Complete Moment Convergence for Sung’s Type Weighted Sums of B -Valued Random Elements. Discrete Dynamics in Nature and Society،Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1103327
Modern Language Association (MLA)
Li, Wei…[et al.]. Complete Moment Convergence for Sung’s Type Weighted Sums of B -Valued Random Elements. Discrete Dynamics in Nature and Society No. 2016 (2016), pp.1-8.
https://search.emarefa.net/detail/BIM-1103327
American Medical Association (AMA)
Li, Wei& Chen, Pingyan& Sung, Soo Hak. Complete Moment Convergence for Sung’s Type Weighted Sums of B -Valued Random Elements. Discrete Dynamics in Nature and Society. 2016. Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1103327
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1103327