On strong law for blockwise M-orthogonal random fields
نویسندگان
چکیده
منابع مشابه
Wittmann Type Strong Laws of Large Numbers for Blockwise m-Negatively Associated Random Variables
Definition 1.2 Let m be a positive integer. A sequence of random variables {Xn, n ≥ 1} is said to be m-negatively associated (m-NA) if for any finite subset of index A = {i1, i2, . . . , in} ⊂ N = {1, 2, 3, . . .}, where n ≥ 2, such that |ik − ij | ≥ m for all 1 ≤ k ̸= j ≤ n, we have that {Xi1 , . . . , Xin} is NA. The concept of m-NA random variables was introduced by Hu et al. [2] where the co...
متن کاملBest Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements
It will be shown and induced that the d-dimensional indices in the Banach spaces version conditions ∑ n(E‖Xn‖/|n|) < ∞ are sufficient to yield limmin1≤ j≤d(nj)→∞(1/ |nα|)∑k≤n ∏d j=1(1− (kj − 1)/nj)Xk = 0 a.s. for arrays of James-type orthogonal random elements. Particularly, it will be shown also that there are the best possible sufficient conditions for multi-indexed independent real-valued ra...
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 Strong Law of Large Numbers for Dependent Random Variables
Throughout this paper, let denote the set of nonnegative integer, let {X,Xn, n ∈ } be a sequence of random variables defined on probability space Ω,F, P , and put Sn ∑n k 1 Xk. The symbol C will denote a generic constant 0 < C < ∞ which is not necessarily the same one in each appearance. In 1 , Jajte studied a large class of summability method as follows: a sequence {Xn, n ≥ 1} is summable to X...
متن کاملStrong invariance principle for dependent random fields
A strong invariance principle is established for random fields which satisfy dependence conditions more general than positive or negative association. We use the approach of Csörgő and Révész applied recently by Balan to associated random fields. The key step in our proof combines new moment and maximal inequalities, established by the authors for partial sums of multiindexed 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: Journal of Inequalities and Applications
سال: 2013
ISSN: 1029-242X
DOI: 10.1186/1029-242x-2013-380