The Conditional H(?)jek-R(?)nyi-Type Inequalities For Conditional PA Sequences And Their Application

Conditional demimartingales is a type of random variables which is wider than martingales.Studying its probability inequalities have great significance to further explore their limit theorems.Conditional PA sequence is a kind of dependent random variables,and the partial sum sequence of conditional PA sequence with mean zero is a demimartingale.Based on a maximal inequality for conditional demimartingales,We use the relationship of conditional PA sequence and conditional demimartingale in hopes of finding the limit results of conditional demimartingale.Our main results are as follows:Firstly.we obtain some conditional Hajek-Renyi-type inequalities for conditional PA sequences,which improves some related results in literature[29].Secondly,we established a strong law of large numbers for conditional PA sequences.Thirdly,we establish a condition for determining whether the conditional expectation of the supremum of a demimartingale is finite almost everywhere.