Complete Convergence for Weighted Sums of Widely Acceptable Random Variables under Sublinear Expectations

Using different methods than the probability space, under the condition that the Choquet integral exists, we study the complete convergence theorem for weighted sums of widely acceptable random variables under sublinear expectation space. We proved corresponding theorem which was extended to the sublinear expectations’ space from the probability space, and similar results were obtained.

On some threshold-one attractive interacting particle systems on homogeneous trees

We consider the threshold-one contact process, the threshold-one voter model and the threshold-one voter model with positive spontaneous death on homogeneous trees $\mathbb{T}_d$ , $d\ge 2$ . Mainly inspired by the corresponding arguments for the contact process, we prove that the complete convergence theorem holds for these three systems under strong survival. When the system survives weakly, complete convergence may also hold under certain transition and/or initial conditions.

Equivalent conditions of complete convergence for weighted sums of ANA random variables

In this paper, the author investigates the complete convergence for weighted sums of asymptotically negatively associated (ANA) random variables with different distributions, and obtains some equivalent conditions of complete convergence theorem for weighted sums as well as summation of ANA cases. These results generalize and improve the corresponding ones obtained by Baum and Katz (1965), Peligrad and Gut (1999) and Cai (2006), respectively.

Complete Convergence of Weighted Sums of ρ Mixing Sequences

Probability limit theory is not only one of the main branches of probability theory, but also important base of others branches and mathematical statistics. In this paper, we discuss the laws of large number and complete convergence of mixing sequence. The paper can be divided into the following two parts. In the first part, we introduce Cesáro uniform integrability and equivalent conditions for sequences of random variable. Then, under these conditions, we establish the weak law of large number and convergence for weighted sums of sequences of random variable of mixing sequence. As an especial example, we obtain the weak law of large number or convergence for mixing sequence. From the course, we can find that Cesáro uniform integrability is also an effective tool for researching the weak law of large number of mixing sequence .In the second part, we investigate a complete convergence theorem of weighted sums of mixing sequence, and prove that the existent results are especial examples for it.

Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums ofρ~-Mixing Random Variables

The equivalent conditions of complete convergence are established for weighted sums ofρ~-mixing random variables with different distributions. Our results extend and improve the Baum and Katz complete convergence theorem. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for sequence ofρ~-mixing random variables is obtained.