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

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

Zbl 1116.60306