Statistical convergence of order $\alpha$ in probability

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$\grave{a}$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.