I-cesaro summability of a sequence of order α of random variables in probability

Abstract

In this paper, we define four types of convergence of a sequence of random variables, namely, I-statistical convergence of order a, I-lacunary statistical convergence of order a, strongly I-lacunary convergence of order a and strongly I-Ces`aro summability of order a in probability where 0 < a < 1. We establish the connection between these notions.