A curious application of the Borel-Cantelli Lemmas, a result of Barndorff-Nielsen, and some open problems
Article Type
Research Article
Publication Title
Stochastic Analysis and Applications
Abstract
For an arbitrary sequence of events {A n ,n≥1} and an integer m ≥ 1 we study the problem whether (Formula presented.) implies either (Formula presented.) or (Formula presented.) It is partially solved using both probabilistic and nonprobabilistic arguments. The First and Second Borel-Cantelli Lemmas are both used to show that the implication holds if m = 1 and an equivalent formulation concerning a real series problem is presented. That the implication does not hold if m = 2 is shown using a real series and it is an open problem for m ≥ 3 Some other open problems are also presented and discussed.
First Page
473
Last Page
479
DOI
10.1080/07362994.2019.1585262
Publication Date
5-4-2019
Recommended Citation
Chandra, Tapas Kumar and Rosalsky, Andrew, "A curious application of the Borel-Cantelli Lemmas, a result of Barndorff-Nielsen, and some open problems" (2019). Journal Articles. 844.
https://digitalcommons.isical.ac.in/journal-articles/844