On conditional Borel-Cantelli lemmas for sequences of random variables
Conditional Borel-Cantelli lemmas were proved by \textit{D. Majerak, W. Nowak} and \textit{W. Zięba} [Int. J. Pure Appl. Math. 20, No. 2, 143--157 (2005; Zbl 1073.60034)] and \textit{B. L. S. Prakasa Rao} [Ann. Inst. Stat. Math. 61, No. 2, 441--460 (2009; Zbl 1314.60054)]. More general versions of the conditional Borel-Cantelli lemmas were given here extending the work of \textit{C. Feng, L. Li} and \textit{J. Shen} [C. R., Math., Acad. Sci. Paris 347, No. 21--22, 1313--1316 (2009; Zbl 1178.60005)] on the weighted Borel-Cantelli lemma and the bilateral inequality of \textit{E. Pancheva, I. K. Mitov} and \textit{K. V. Mitov} [Stat. Probab. Lett. 79, No. 3, 390--395 (2009; Zbl 1158.60019)].
scientific article; zbMATH DE number 6125374