Sentence examples for maximal inequality and from inspiring English sources

Newman and Wright [3] have extended various results including Doob's maximal inequality and Doob's upcrossing inequality to the case of demimartingales.

The aim of this paper is to study the complete moment convergence of moving average process of random sequence under the assumption that the random variables satisfy the Rosenthal type maximal inequality and the weak mean dominating condition.

In this paper we will establish the complete moment convergence for a moving average process generated by the class of random variables satisfying a Rosenthal-type maximal inequality and a weak mean dominating condition.

In this paper, by the Kolmogorov type maximal inequality and Stein's method, we establish the result of the law of the iterated logarithm for LNQD sequence with less restriction of moment conditions.

In this paper, we establish the complete moment convergence of a moving average process generated by the class of random variables satisfying a Rosenthal-type maximal inequality and a weak mean dominating condition with a mean dominating variable.

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 a sequence of mean zero associated random variables is a demimartingale.

In the case (d=1), Nam, Hu, and Volodin [11] introduced the concept of m-AANA and investigated maximal inequalities and strong law of large numbers.

In Section 2, by the Kolmogorov type maximal inequalities and Stein's method, we obtain the law of the iterated logarithm for strictly stationary LNQD sequence with finite variance.

We refer to Bradley [1] (which assumes in the central limit theorem), Bryc and Smoleński [2], Goldie and Greenwood [3] (which assumes ), and Yang [4] for moment inequalities and the strong law of large numbers, Wu [5, 6], Wu and Jiang [7], Peligrad and Gut [8], and Gan [9] for almost sure convergence and Utev and Peligrad [10] for maximal inequalities and the invariance principle.

Eghbal et al. [6] derived two maximal

We refer only to some of them: Roussas [2] for the central limit theorem for weakly stationary fields; Zhang and Wen [3] for the Rosenthal maximal inequality; Xia and Chu [4] for the convergence rates in the law of iterated logarithm and the Rosenthal maximal inequality for identically distributed random variables; Li [5] for the convergence rates in the law of iterated logarithm.