The strong laws of large numbers for positive measurable operators and applications

2017 ◽  
Vol 124 ◽  
pp. 110-120 ◽  
Author(s):  
Nguyen Van Quang ◽  
Do The Son ◽  
Le Hong Son
Keyword(s):  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Measurable Operators

Exact strong laws of large numbers for independent random fields

2018 ◽  
Vol 66 (2) ◽  
pp. 179-188 ◽  
Author(s):  
Paweł Kurasiński ◽  
Przemysław Matuła ◽  
André Adler
Keyword(s):  
Random Fields ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers

scholarly journals On Chung-Teicher type strong law for arrays of vector-valued random variables

2004 ◽  
Vol 2004 (9) ◽  
pp. 443-458
Author(s):  
Anna Kuczmaszewska
Keyword(s):  
Banach Space ◽  
Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Random Elements ◽  
Vector Valued

We study the equivalence between the weak and strong laws of large numbers for arrays of row-wise independent random elements with values in a Banach spaceℬ. The conditions under which this equivalence holds are of the Chung or Chung-Teicher types. These conditions are expressed in terms of convergence of specific series ando(1)requirements on specific weighted row-wise sums. Moreover, there are not any conditions assumed on the geometry of the underlying Banach space.

Exact strong laws of large numbers for ratios of the smallest order statistics

2019 ◽  
Vol 152 ◽  
pp. 69-73
Author(s):  
Przemysław Matuła ◽  
Paweł Kurasiński ◽  
André Adler
Keyword(s):  
Order Statistics ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers
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