Strong convergence of weighted sums of random elements through the equivalence of sequences of distributions
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Publication:1103937
DOI10.1016/0047-259X(88)90054-1zbMath0646.60008MaRDI QIDQ1103937
Carlos Matrán, Juan Antonio Cuesta
Publication date: 1988
Published in: Journal of Multivariate Analysis (Search for Journal in Brave)
strong law of large numbersSkorokhod representation theoremToeplitz sequence of real numbersweakly equivalent sequences of probability measures
Probability measures on topological spaces (60B05) Strong limit theorems (60F15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)
Related Items (10)
On conditional compactly uniform \(p\)th-order integrability of random elements in Banach spaces ⋮ Uniform integrability of sequences of random elements with respect to weak topologies and weak integrals ⋮ 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 ⋮ Compactly uniform Bochner integrability of random elements ⋮ A strong law of large numbers for non identically distributed Pettis integrable random sets in a general Banach space ⋮ Law of large numbers and Ergodic Theorem for convex weak star compact valued Gelfand-integrable mappings ⋮ Summary: On the strong laws of large numbers for double arrays of random variables in convex combination spaces ⋮ A review on strong convergence of weighted sums of random elements based on Wasserstein metrics ⋮ \(\mathfrak{S}\)-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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- Limit theorems for weighted sums of random elements in separable Banach spaces
- On the strong law of large numbers for pairwise independent random variables
- A note on convergence of weighted sums of random variables
- Stochastic convergence of weighted sums of random elements in linear spaces
- Stochastic convergence of weighted sums in normed linear spaces
- The law of large numbers and the central limit theorem in Banach 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
- Convergence of stochastic processes
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