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ON THE STRONG LAW OF LARGE NUMBERS
Acta Mathematica Scientia, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qiu, Dehua, Gan, Shixin
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Explicit Stable Strong Laws of Large Numbers
Calcutta Statistical Association Bulletin, 1994In this article it is shown, through a very interesting class of random variables, how one may go about explicitly obtaining constants in order to obtain a stable strong law of large numbers. The question at hand is, not when we can find constants an and bn so that our sequence of i. i.d. random variables obeys this type of strong law of large numbers,
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On the strong law of large numbers
Statistics & Probability Letters, 1969The connection between general moment conditions and SLLN for identically distributed random variables is examined. Let \(f(x)\) be an positive even continuous function strictly increasing in the region \(x>0\) and \(f(+\infty)=\infty\), \(a_n=f^{-1}(n)\) where \(f^{-1}\) is the inverse of \(f\). The following two statements are proved. 1) Let \(\{X_n\}
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The Strong Law of Large Numbers
1991In this chapter and in the next one, we present respectively the strong law of large numbers and the law of the iterated logarithm for sums of independent Banach space valued random variables. In this study, the isoperimetric approach of Section 6.3 demonstrates its efficiency. We only investigate extensions to vector valued random variables of some of
Michel Ledoux, Michel Talagrand
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A strong law of large numbers for U-statistics
Journal of Statistical Planning and Inference, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christofides, Tasos C. +1 more
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Bernoulli's Law of Large Numbers and the Strong Law of Large Numbers
Theory of Probability & Its Applications, 2016We discuss the connection between the law of large numbers and the strong law of large number for sums of independent random variables. The mathematical content of these laws and their connection with mathematical statistics problems is compared.
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The Strong Law of Large Numbers
1994Abstract This chapter focuses largely on methods of proof of the strong law, building on the fundamental convergence lemma. It covers Kolmogorov's three‐series theorem, strong laws for martingales, and random weighting. Then a range of strong laws are proved for mixingales and for near‐epoch dependent and mixing processes.
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A generalized strong law of large numbers
Probability Theory and Related Fields, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Colubi, Ana +3 more
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The Strong Law of Large Numbers
199615.1 This section gives some fundamental definitions in the theory of probability, such as the definitions of a probability space and a random variable.
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Strong limit theorems: the strong law of large numbers
1995Abstract The second part of this lemma was found by Erdös and Renyi. In a traditional formulation of the Borel-Cantelli lemma the condition of pairwise independence is replaced by the stronger condition of the mutual independence of the events A1, ... , An for every n.
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