Abstract
In this paper, by using the Rosenthal-type maximal inequality for ψ-mixing random variables, we obtain the Khintchine-Kolmogorov-type convergence theorem, which can be applied to establish the three series theorem and the Chung-type strong law of large numbers for ψ-mixing random variables. In addition, the strong stability for weighted sums of ψ-mixing random variables is studied, which generalizes the corresponding one of independent random variables. MSC:60F15.
Highlights
Let (, F, P) be a fixed probability space
We will further study the strong stability for weighted sums of ψ-mixing random variables, which generalizes corresponding one of independent sequences
The main results of the paper depend on the following important lemma - Rosenthal-type maximal inequality for ψ-mixing random variables
Summary
Let ( , F , P) be a fixed probability space. The random variables we deal with are all defined on ( , F , P). The main purpose of this paper is to establish the Khintchine-Kolmogorov-type convergence theorem, which can be applied to obtain the three series theorem and the Chung-type strong law of large numbers for ψ-mixing random variables. For independent and identically distributed random variable sequences, Jamison et al [ ] proved the following theorem. We will further study the strong stability for weighted sums of ψ-mixing random variables, which generalizes corresponding one of independent sequences.
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