[PDF] Top 20 Complete convergence and complete moment convergence for randomly weighted sums of martingale difference sequence

... for weighted sums of extended negatively depen- dent (END) random variable sequence was investigated by Shen et ...type convergence rate in the Marcinkiewicz–Zygmund strong law for ...the ... See full document

... the moment inequalities for the ϕ-mixing random variables and gave its application to the complete convergence for this stochastic process; Yu [] ob- tained the complete convergence ... See full document

... of martingale differences can be found in many books such as Stout [], Hall and Heyde [], Shiryaev [], Gut [], and so ...the complete convergence of martingale arrays; Stoica [, ] ... See full document

... partial sums of randomly weighted random ...the complete convergence of partial sums of randomly weighted independent sequences in Banach spaces; Thanh et ... See full document

... of complete convergence, it has been an important basic tool to study the convergence in probability and ...the complete convergence of Hsu and Robbins [], Chow [] first investigated ... See full document

... the convergence properties of this wider m- NA ...the convergence properties for sequences of m-NA random ...the complete convergence for weighted sums of identically distributed ... See full document

... The complete convergence has a relatively complete development in probability limit ...of complete convergence was raised by Hsu and Robbins [], and Chow [] established ... See full document

... partial sums), Bradley [, ] (equivalent mixing conditions and various limit properties), Peligrad [] (a moment inequality of maximal partial sums for sequences) and Peligrad and Gut [] (a ... See full document

... The concept of NSD random variables was introduced by Hu [], which was based on the class of superadditive functions. Hu [] gave an example illustrating that NSD does not imply NA, and he posed an open problem whether ... See full document

... applying moment inequality of negatively dependent (ND) random variables which obtained by Asadian et ...the complete convergence theorem for weighted sums of arrays of rowwise ND ... See full document

... The complete moment convergence of weighted sums for arrays of rowwise ϕ-mixing random variables is ...using moment inequality and truncation method, the sufficient conditions for ... See full document

... a sequence of identically distributed ρ ∗ -mixing random variables with suitable moment ...The moment conditions for the cases α < rp and α > rp are ...The moment conditions for α = rp ... See full document

... concerning complete convergence for martingale arrays obtained in the one-dimensional case, we refer to Lagodowski and Rychlik [], Elton [], Lesigne and Volny [], Stoica [] and Ghosal and ... See full document

... depending on the sequence of random variables in each row are bounded. So Corollary 3.6 holds for arrays of rowwise ρ ∗ -mixing random variables satisfying this additional condition. Zhu 12 obtained only 2.26 in ... See full document

... Inspired by the above results, the purpose of this paper is to study a general law of complete moment convergence for self-normalized sums. Our main result is as follows. Theorem 1.1. Suppose ... See full document

... Remark 1.3. The proof of Theorem D was based on Theorem 1 of Chen et al. 16, which gave sufficient conditions about complete convergence for NA random variables. So far, it is not known whether the result of ... See full document

... discussed the complete convergence for B-valued independent random elements.Yu[ll] ha co,sidered the complete convergence for martingale difference sequences, PeligradI7 and Shao[S} have[r] ... See full document

... Moreover, they proved that the sequence of arithmetic means of independent identically distribution (i.i.d.) random variables converges completely to the expected value if the variance of the summands is finite. ... See full document

... some complete convergence and complete moment convergence theorems for independent random variables to the case of negatively associated random variables without necessarily imposing ... See full document

... strong convergence for weighted sums of arrays of ANA random variables without assumption of identical distribution and obtain some im- proved results ...so-called complete moment ... See full document