A note on the strong law of large numbers for associated sequences
نویسندگان
چکیده
منابع مشابه
A Note on the Strong Law of Large Numbers
Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...
متن کاملA note on the strong law of large numbers for associated sequences
assuming of course that the covariance exists. The infinite sequence {Xn, n ≥ 1} is said to be associated if every finite subfamily is associated. The concept of association was introduced by Esary et al. [1]. There are some results on the strong law of large numbers for associated sequences. Rao [4] developed the Hajek-Renyi inequality for associated sequences and proved the following theorem....
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N lim 1( 1: f(nkx)) = 0, N-N k_l or roughly speaking the strong law of large numbers holds for f(nkx) (in fact the authors prove that Ef(nkx)/k converges almost everywhere) . The question was raised whether (2) holds for any f(x) . This was known for the case nk=2k( 2) . In the present paper it is shown that this is not the case . In fact we prove the following theorem . THEOREM 1 . There exist...
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In the following work we present a proof for the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise independence. Let be a double sequence of pairwise negatively dependent random variables. If for all non-negative real numbers t and , for 1 < p < 2, then we prove that (1). In addition, it also converges to 0 in ....
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For a sequence of pairwise negative quadrant dependent random variables {Xn, n ≥ 1}, conditions are given under which normed and centered partial sums converge to 0 almost certainly. As special cases, new results are obtained for weighted sums { ∑n j=1 ajXj , n ≥ 1} where {an, n ≥ 1} is a sequence of positive constants and the {Xn, n ≥ 1} are also identically distributed. A result of Matu la [1...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2005
ISSN: 0161-1712,1687-0425
DOI: 10.1155/ijmms.2005.3195