Complete Convergence and the Law of Large Numbers
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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; 1 X i i is a strictly stationary Gaussian sequence which has a bounded positive every t, then 1 1 1 m M ; 1 n X n . Thus, is a -mixing sequence. -mixing is similar to -mixing, but both are quite different. k is defined by (1.1) with index sets restricted to subsets S of 1,n T and subsets of , , , n k n k N . On the other hand, -mixing sequen...
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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Our purpose in this article is to show that if P is any probability measure on N such that P({ν}) > 0 for every ν ∈ N, then the set of all sequences of random variables on the probability measure space (N,P(N),P) which are in L(N,P) and satisfy the law of large numbers is Π3-complete.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1947
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.33.2.25