[PDF] Top 20 On Strong Law of Large Numbers for Dependent Random Variables

... Since the definition of complete convergence was introduced by Hsu and Robins, there have been many authors who devote themselves to the study of the complete convergence for sums of independent and dependent RVs ... See full document

... the strong law of large numbers for independent and identically distributed random variables by embedding ...the strong law of large numbers for ... See full document

... several strong laws of large numbers for general random variables and obtain the growth rate of the partial ...a strong law of large numbers for negatively ... See full document

... weak law of large numbers ...phrases. Random element, Banach spaces, weak law of large numbers, strong law of large ... See full document

... of large numbers, were obtained for independent random sets or fuzzy random sets in the past decades, and little is known of dependent random sets or fuzzy random sets ... See full document

... Strong law of large numbers is a fundamental theory in probability and ...this law is very different from additive ...the strong law of large numbers under ... See full document

... Remark 1.4. Chow 1 proved a maximal inequality for submartingales. Newman and Wright 2 extended Doob’s maximal inequality and upcrossing inequality to the case of demimartingales, and pointed out that the partial sum of ... See full document

... a strong law of large numbers for α = 0 was proven for a simple random walk by Dvoretzky and Erd˝os in ...the strong convergence (5) is proven for all α ≥ 0 (up to a gap in the ... See full document

... independent random vari- ables can be applied to sequences consisting of independent ...the strong laws of large numbers to blockwise-martingale difference arrays in Banach ...of random ... See full document

... the strong law of large numbers for general weighted sums of asymptotically almost negatively associated random variables (AANA, in short) with non-identical ...Marcinkiewicz ... See full document

... of large numbers for orthogonal random variables or Banach space-valued random elements are investigated by several ...a strong law of large numbers of a ... See full document

... Since the conception of PND sequences contains independent and negatively associated sequences, which have a lot of applications, e.g. in reliability theory, Percolation theory and multivariate statistical analysis, ... See full document

... = ∑ X n = S n ( ) / n . Landers and Rogge [8] proved a strong law of large numbers (SLLN) for pairwise independent and strongly uniformly integrable r.v.’s. Chandra and Goswami [3] proved a ... See full document

... the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise ...negatively dependent ... See full document

... the strong law of large numbers for asymptotically negatively associated random variables are ...Marcinkiewicz strong law of large numbers for ... See full document

... of large numbers at different kinds of conditions and different kinds of ...set-valued random theory, the theory of set-valued random variables and their applications have become one of ... See full document

... the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically ...of strong ... See full document

... The question underlying the present work is how one may refine Theorem CG1 to give more information on the law of { X n } . We recall the classical answer, the strong law of large ... See full document

... Jain [3] obtained a uniform strong law of large numbers for sequences of i.i.d, random elements in separable Banach spaces of type 2 which would yield 1.2 with p 1 for an array of i.i.d,[r] ... See full document

... STRONG LAWS OF LARGE NUMBERS FOR ARRAYS OF ROWWISE INDEPENDENT RANDOM ELEMENTS ROBERT LEE TAYLOR Department of Statistics University of Georgia Athens, GA 30602 U.S.A... TIEN.CHUNG HU De[r] ... See full document