Statistical convergence of order $\alpha$ in probability

Abstract

In this paper ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order $\alpha$ in probability, strong $p$-Ces$\grave{\mbox{a}}$ro summability of order $\alpha$ in probability, lacunary statistical convergence or $S_{\theta}$-convergence of order $\alpha$ in probability, ${N_{\theta}}$-convergence of order $\alpha$ in probability have been introduced and their certain basic properties have been studied.