The convergence rate for the strong law of large numbers: General lattice distributions
نویسندگان
چکیده
منابع مشابه
On the Convergence Rate of the Law of Large Numbers for Sums of Dependent Random Variables
In this paper, we generalize some results of Chandra and Goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). Furthermore, we give Baum and Katz’s [1] type results on estimate for the rate of convergence in these laws.
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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 ...
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in this paper, we generalize some results of chandra and goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). furthermore, we give baum and katz’s [1] type results on estimate for the rate of convergence in these laws.
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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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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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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1987
ISSN: 0304-4149
DOI: 10.1016/0304-4149(87)90123-2