A Strong Invariance Theorem for the 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 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 and Functional Central Limit Theorem
20.1. Additional technical results on weak convergence Given two metric spaces S1, S2 and a measurable function f : S1 → S2, suppose S1 is equipped with some probability measure P. This induces a probability measure on S2 which is denoted by Pf−1 and is defined by Pf−1(A) = P(f−1(A) for every measurable set A ⊂ S2. Then for any random variable X : S2 → R, its expectation EPf −1 [X] is equal to ...
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 کاملthe strong law of large numbers for pairwise negatively dependent random variables
in this paper, strong laws of large numbers (slln) are obtained for the sums ƒ°=nii x1, undercertain conditions, where {x ,n . 1} n is a sequence of pairwise negatively dependent random variables.
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: The Annals of Probability
سال: 1978
ISSN: 0091-1798
DOI: 10.1214/aop/1176995488