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The Weak and Strong Laws of Large Numbers
2023William L. Dunn, J. Kenneth Shultis
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Weak Laws of Large Numbers in Some Non-Commutative Spaces
Bulletin of the London Mathematical Society, 2000Summary: We prove weak laws of large numbers for freely independent, uniformly bounded and non-identically distributed random variables belonging to non-commutative Ciach and, in particular, Lorentz \(L^p\)-spaces.
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On the Weak Law of Large Numbers for D(0,1).
1979Abstract : Weak laws of large numbers are obtained for random elements in D(0,1) where the convergence is in the sup-norm topology. For identically distributed random elements satisfying a compact integral condition, the weak law of large numbers holding pointwise is shown to be necessary and sufficient for the weak law of large numbers. In addition to
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Strong laws of large numbers under weak assumptions with application
IEEE Transactions on Automatic Control, 2000Summary: The employment of ``strong laws of large numbers'' is instrumental to the analysis of system estimation and identification strategies. However, the vast bulk of such laws, as presented in the wider literature, assume independence or at least uncorrelatedness of random components, and these assumptions are quite restrictive from an engineering ...
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Characterization of typep Banach spaces by the weak law of large numbers
Wuhan University Journal of Natural Sciences, 2002The author establishes an \(L^r\) convergence theorem and a weak law of large numbers for weighted sums \(\sum_{j=1}^{k_n}a_{nj}X_{nj}\), where for every \(n\), \(X_{nj}\), \(1\leq j \leq k_n\), are independent zero mean random elements in a Banach space of type \(p\).
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Weak law of large numbers for I.I.D. fuzzy random variables
Kybernetika, 2007For fuzzy random variables, the authors prove two theorems which are counterparts of the well known Kolmogorov-Feller weak law of large numbers and its generalisation by \textit{A. Gut}, ``An extension of the Kolmogorov-Feller weak law of large numbers with an application to the St. Petersburg game,'' J. Theor. Probab.
Dug Hun Hong, Kyung Tae Kim
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A Minimax Analogue of the Weak Law of Large Numbers
Theory of Probability & Its Applications, 1971openaire +1 more source