On Hàjek-Rènyi-type inequality for conditionally negatively associated random variables and its applications (Q2890576)

The Hájek-Rènyi inequality is extended from the negative association to the conditional negative association. For this purpose, first the conditional Rosenthal type inequality for the conditional negative association is proved. As an application of the extended Hájek-Rènyi inequality the integrability of the supremum and a strong law of large numbers for conditionally negatively associate random variables are obtained. The condiitonally centered sequence of random variables is one from the initial terms in this paper.