$\mathcal{I}$-Cesaro Summability of a Sequence of Order $\alpha$ of Random Variables in Probability

Authors : Ömer Kişi, Erhan Güler

Pages : 157-161

Doi:10.33401/fujma.480808

View : 13 | Download : 9

Publication Date : 2018-12-25

Article Type : Research

Abstract :In this paper, we define four types of convergence of a sequence of random variables, namely, $\mathcal{I}$-statistical convergence of order $ \alpha $, $\mathcal{I}$-lacunary statistical convergence of order $\alpha $, strongly $\mathcal{I}$-lacunary convergence of order $\alpha $ and strongly $ \mathcal{I}$-Cesaro summability of order $\alpha $ in probability where $ 0<\alpha <1$. We establish the connection between these notions.
Keywords : Probability, Lacunary, Ideal convergence