On complete convergence of weighted sums of random elements

Cabrera, Manuel Ordóñez; Sung, Soo Hak

doi:10.1081/sap-120002420

Stochastic Analysis and Applications

2002

DOI: 10.1081/sap-120002420

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On complete convergence of weighted sums of random elements

Manuel Ordóñez Cabrera

Soo Hak Sung

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Cited by 2 publications

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On Chung’s Law of Large Numbers on Simply Connected Step 2-Nilpotent Lie Groups

Neuenschwander

2013

J Math Sci

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Ordóñez Cabrera and Sung (2002) have proved that under certain "moment" conditions, for triangular arrays of weighted Banach-valued random variables, a.s. convergence, convergence in L 1 , convergence in probability, and complete convergence to 0 are equivalent, thus giving a variant of Chung's law of large numbers. We extend their result (under slightly sharper technical conditions) to symmetric random variables on simply connected step 2-nilpotent Lie groups.

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On Chung’s Law of Large Numbers on Simply Connected Step 2-Nilpotent Lie Groups

Neuenschwander

2013

J Math Sci

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Weighted M-estimators for multivariate clustered data

Asri

Blanke

Gabriel

2016

Statistics & Probability Letters

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On complete convergence of weighted sums of random elements

Cited by 2 publications

References 11 publications

On Chung’s Law of Large Numbers on Simply Connected Step 2-Nilpotent Lie Groups

On Chung’s Law of Large Numbers on Simply Connected Step 2-Nilpotent Lie Groups

Weighted M-estimators for multivariate clustered data

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