Statistical convergence of order α in probability

Abstract

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

Keywords

• Statistical convergence of order α in probability
• Strong p-Cesàro summability of order α in probability
• Lacunary statistical convergence or Sθ-convergence of order α in probability
• Nθ-convergence of order α in probability