Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables

In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.

Complete response of gallbladder cancer treated with gemcitabine and cisplatin chemotherapy combined with durvalumab:A case report and review of literature

BACKGROUND Gallbladder cancer(GBC)is the most common and aggressive subtype of biliary tract cancer(BTC)and has a poor prognosis.A newly developed regimen of gemcitabine,cisplatin,and durvalumab shows promise for the treatment of advanced BTC.However,the efficacy of this treatment for GBC remains unclear.CASE SUMMARY In this report,we present a case in which the triple-drug regimen exhibited marked effectiveness in treating locally advanced GBC,thus leading to a long-term survival benefit.A 68-year-old man was diagnosed with locally advanced GBC,which rendered him ineligible for curative surgery.Following three cycles of therapy,a partial response was observed.After one year of combined therapy,a clinical complete response was successfully achieved.Subsequent maintenance therapy with durvalumab monotherapy resulted in a disease-free survival of 9 months for the patient.The patient experienced tolerable toxicities of reversible grade 2 nausea and fatigue.Tolerable adverse events were observed in the patient throughout the entirety of the treatment.CONCLUSION The combination of gemcitabine and cisplatin chemotherapy with durvalumab was proven to be an effective treatment approach for advanced GBC,with manageable adverse events.Further research is warranted to substantiate the effectiveness of the combined regimen in the context of GBC.

Passive activity enhances residual control ability in patients with complete spinal cord injury

Patients with complete spinal cord injury retain the potential for volitional muscle activity in muscles located below the spinal injury level.However,because of prolonged inactivity,initial attempts to activate these muscles may not effectively engage any of the remaining neurons in the descending pathway.A previous study unexpectedly found that a brief clinical round of passive activity significantly increased volitional muscle activation,as measured by surface electromyography.In this study,we further explored the effect of passive activity on surface electromyographic signals during volitional control tasks among individuals with complete spinal cord injury.Eleven patients with chronic complete thoracic spinal cord injury were recruited.Surface electromyography data from eight major leg muscles were acquired and compared before and after the passive activity protocol.The results indicated that the passive activity led to an increased number of activated volitional muscles and an increased frequency of activation.Although the cumulative root mean square of surface electromyography amplitude for volitional control of movement showed a slight increase after passive activity,the difference was not statistically significant.These findings suggest that brief passive activity may enhance the ability to initiate volitional muscle activity during surface electromyography tasks and underscore the potential of passive activity for improving residual motor control among patients with motor complete spinal cord injury.

On the rate of complete convergence for weighted sums of NSD random variables and an application

In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.

Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.

COMPLETE MOMENT CONVERGENCE FOR L^P-MIXINGALES

In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.

Complete Moment Convergence for Arrays of Rowwise Negatively Associated Random Variables

In this paper, the authors present some new results on complete moment convergence for arrays of rowwise negatively associated random variables. These results improve some previous known theorems.

On Complete Convergence for Arrays of Rowwise Strong Mixing Random Variables

In this paper, we present a general method to prove the complete conver- gence for arrays of rowwise strong mixing random variables, and give some results on complete convergence under some suitable conditions. Some Marcinkiewicz-Zygmund type strong laws of large numbers are also obtained.

Almost Sure Convergence and Complete Convergence for the Weighted Sums of Martingale Differences

Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.

On complete convergence for Stout's type weighted sums of NOD sequence

In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup.The more optimal moment condition is given. The main results also hold for END sequence.

Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Extended Negatively Dependent Random Variables

By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. （Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8： 49-76） and Liang （Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48： 317-325）.

Exponential Inequalities and Complete Convergence for Extended Negatively Dependent Random Variables

Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequality for negative dependent sequence.Communications of the Korean Mathematical Society, 2007, 22(2): 315-321) and Nooghabi and Azarnoosh(Exponential inequality for negatively associated random variables. Statistical Papers, 2009, 50(2): 419-428). We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which improves the corresponding ones of Kim and Kim,and Nooghabi and Azarnoosh.

Complete moment convergence for ND random variables under the sub-linear expectations

In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of results on complete moment convergence for ND random variables under the sub-linear expectations.

COMPLETE CONVERGENCE FOR A CLASS OF MIXING SEQUENCES

Under some conditions on probability, the author obtains some results on the complete convergence for partial sums of not necessary identically distributed p-mixing se- quences, and the complete convergence for partial sums of B-valued martingale differences is also studied. As application the author gives the corresponding results on the complete convergence for randomly indexed partial sums.

COMPLETE CONVERGENCE THEORY OF THE CONTACT PROCESS ON T_d×Z

The author considers the contact process on a branching plane Td×Z, which is the product of a regular tree Td and the line Z. It is shown that above the second critical point, the complete convergence theory holds.

MAXIMAL INEQUALITY AND COMPLETE CONVERGENCES OF NON-IDENTICALLY DISTRIBUTED NEGATIVELY ASSOCIATED SEQUENCES

A maximal inequality for the partial sum of NA sequence is constructed. By using this inequality the complete convergence rates in the strong laws for a class of dependent random variables for weighted sums are discussed. The results obtained extend the results of Liang （1999, 2000）.

On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables

We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions.Consequently,we get the results for many dependent structures,such as END,ϱ^(*)mixing,ϱ^(-)mixing andφ-mixing,etc.

Complete Convergence of Weighted Sums for Arrays of Rowwise m-negatively Associated Random Variables

In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables are established. These results generalize and complement some known conclusions.