On inverse moments of nonnegative weakly convergent random variables. (Chinese. English summary) Zbl 1141.60309

Hu, Shuhe; Chen, Guijing; Wang, Xuejun; Chen, Enbing

Acta Math. Appl. Sin. 30, No. 2, 361-367 (2007).

Summary: The authors give sufficient conditions under which \(\lim\limits_{n \to \infty}(1+EX_n)^\alpha E\frac{1}{(1+X_n)^\alpha}=1\) for sequences of nonnegative weakly convergent random variables when their \((2+\delta)\)th moments are finite and \(\alpha >0\) . It generalizes the results of A. Kaluszka and A. Okolewski [Statist. Probab. Lett. 66, 45–50 (2004; Zbl 1116.60306)] and gives complete proofs for their Theorem \(3\) and Theorem \(4\).

MSC:

60E15	Inequalities; stochastic orderings
60F05	Central limit and other weak theorems

Keywords:

weak convergence; inverse moments; Lyapunov condition

Citations:

Zbl 1116.60306