Statistical convergence of order αα in probability

In this paper the ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order αα in probability, strong pp-Cesàro summability of order αα in probability, lacunary statistical convergence or SθSθ-convergence of order αα in probability, and NθNθ-convergence of order αα in probability have been introduced and their certain basic properties have been studied.