Strong law of large numbers for sums of products
نویسندگان
چکیده
منابع مشابه
Strong Law of Large Numbers for Sums of Products
Let X;Xn, n ≥ 1, be a sequence of independent identically distributed random variables. We give necessary and sufficient conditions for the strong law of large numbers n−k/p ∑ 1≤i1 x as x → ∞, without further conditi...
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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.
متن کاملA 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 کاملMARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES
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 ....
متن کاملon 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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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1996
ISSN: 0091-1798
DOI: 10.1214/aop/1065725194