Conditional acceptability of random variables

• Main Authors: Tasos C Christofides, István Fazekas, Milto Hadjikyriakou
• Format: Article
• Language: English
• Published: SpringerOpen 2016-06-01
• Series: Journal of Inequalities and Applications
• Subjects: F $\mathcal{F}$ -acceptable random variables; conditional complete convergence; exponential inequalities
• Online Access: http://link.springer.com/article/10.1186/s13660-016-1093-1

Abstract Acceptable random variables introduced by Giuliano Antonini et al. (J. Math. Anal. Appl. 338:1188-1203, 2008) form a class of dependent random variables that contains negatively dependent random variables as a particular case. The concept of acceptability has been studied by authors under various versions of the definition, such as extended acceptability or wide acceptability. In this paper, we combine the concept of acceptability with the concept of conditioning, which has been the subject of current research activity. For conditionally acceptable random variables, we provide a number of probability inequalities that can be used to obtain asymptotic results.