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

Year 2018, Volume: 1 Issue: 2, 157 - 161, 25.12.2018

Ömer Kişi Erhan Güler

https://doi.org/10.33401/fujma.480808

Cited By: 3

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

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