A review on strong convergence of weighted sums of random elements based on Wasserstein metrics

DOI10.1016/0378-3758(92)90162-LzbMath0752.60029OpenAlexW1981254318MaRDI QIDQ1194002

Carlos Matrán, Juan Antonio Cuesta

Publication date: 27 September 1992

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-3758(92)90162-l

zbMATH Keywords

strong convergencestrong law of large numberssummability methodsGlivenko-Cantelli theoremBanach-valued random elementsWasserstein's metric

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Strong limit theorems (60F15) Probability theory on linear topological spaces (60B11) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (4)

Pointwise ergodic theorem and strong law of large numbers for random points in a metric space with negative curvature ⋮ Strong Law of Large Numbers for Stationary Sequences of Random Upper Semicontinuous Functions ⋮ A strong law of large numbers for non identically distributed Pettis integrable random sets in a general Banach space ⋮ \(\mathfrak{S}\)-uniform scalar integrability and strong laws of large numbers for Pettis integrable functions with values in a separable locally convex space

Cites Work

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• On the laws of large numbers for nonnegative random variables
• Limit theorems for weighted sums of random elements in separable Banach spaces
• A note on convergence of weighted sums of random variables
• Strong convergence of weighted sums of random elements through the equivalence of sequences of distributions
• Some asymptotic theory for the bootstrap
• Stochastic convergence of weighted sums in normed linear spaces
• Convergence of weighted sums of tight random elements
• Laws of large numbers for tight random elements in normed linear spaces
• An Extension of Skorohod's Almost Sure Representation Theorem
• An elementary proof of the strong law of large numbers
• Convergence of weighted averages of independent random variables
• Some Results on the Complete and Almost Sure Convergence of Linear Combinations of Independent Random Variables and Martingale Differences

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