A Note on Chung's Strong Law of Large Numbers
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 کاملOn the Strong Law of Large Numbers
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...
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....
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 کاملStrong law of large numbers on graphs and groups
We introduce the notion of the mean-set (expectation) of a graph(group-) valued random element ξ and prove a generalization of the strong law of large numbers on graphs and groups. Furthermore, we prove an analogue of the classical Chebyshev’s inequality for ξ. We show that our generalized law of large numbers, as a new theoretical tool, provides a framework for practical applications; namely, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1998
ISSN: 0022-247X
DOI: 10.1006/jmaa.1998.5740