[PDF] Top 20 Strong Law of Large Numbers under an Upper Probability

... with probability 1 under  (that is, quasi surely), and furthermore, if  is null-additive, then that limit in- ferior attains the submean and the limit superior attains the supermean quasi surely, ...the ... See full document

... the strong law of large ...the strong law of large numbers for sequences of random variables by using a H´ajek-R´enyi-type maximal ...the strong law of ... See full document

... The aim of this paper is to investigate inequalities for sums of random fields and the strong law of large numbers of arbitrary random fields taking values in a Banach space. In Section , we ... See full document

... the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise ...real numbers t and E X p log + X < ∞ , for 1 < ... 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 sequence of orthogonal ... See full document

... the strong law of large numbers for the number of sites visited exactly j times up to time ...odd numbers, Corollary 3 can be reduced to the singleton case, once we know the ... See full document

... the strong law of large numbers and the Shannon-McMillan the- orem for finite Markov chains indexed by an infinite tree with assumption () ...Then under the assumption of Lemma , for ... See full document

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

... in probability and ...of large numbers at different kinds of conditions and different kinds of ...a strong law of large numbers for independent and identically distributed ... See full document

... the strong law of large numbers for a class of random variables satisfying the maximal moment inequality with exponent ...Kolmogorov strong law of large numbers and ... 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 law of ... 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

... The strong law of large numbers for NA RVs will be established in Section ...Hus-Robbins-type law of large numbers will be presented in Sections 4 and 5, ... See full document

... spaces under the assumption that the weak law of large numbers ...weak law of large numbers, strong law of large ... 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 dependent ... See full document

... variables under the conditions E|X| p log + |X| r+1 < ∞, E|X| p log + |X| r−1 < ∞, respectively, thus, extending Choi and Sung’s result [1] of the one-dimensional ... See full document

... a large number of limit results for pairwise NQD random variable ...Kolmogorov strong law of large num- bers, Wang et ...Marcinkiewicz strong law of large numbers ... See full document

... the strong law of large numbers; Wang et ...weak law of large numbers; Wu [] obtained the strong convergence properties of Jamison weighted sums, the three series ... See full document

... In Chapter 3 we will also discuss, for ARMA models, the strong law of large numbers, methods of identification and their relationship to the central limit theorem. * The conditions required ... See full document

... Motivated by the work of Sung [], the aim of this paper is to obtain the complete con- vergence under more general moment conditions. Our main result includes the Baum and Katz [] complete convergence and the ... See full document