ROUGH STATISTICAL CONVERGENCE ON TRIPLE SEQUENCE OF RANDOM VARIABLES IN PROBABILITY

Abstract

This paper aims a further improvement from the works of Phu [9], Aytar [1] and Ghosal [7]. We propose a new apporach to extend the application area of rough statistical convergence usually used in triple sequence of real numbers to the theory of probability distributions. The introduction of this concept in probability of rough statistical convergence, rough strong Cesaro summable, rough lacunary statistical convergence, rough N-theta- convergence, rouugh lambda- statistical convergence and rough strong (V, lambda) - summable generalize the convergence analysis to accommodate any form of distribution of random variables. Among these six concepts in probability only three convergences are distinct rough statistical convergence, rough lacunary statistical convergence and rough lambda- statistical convergence where rough strong Cesaro summable is equivalent to rough statistical convergence, rough N-theta- convergence is equivalent to rough lacunary statistical convergence, rough strong (V, lambda) - summable is equivalent to rough lambda- statistical convergence. Basic properties and interrelations of above mentioned three distinct convergences are investigated and some observations are made in these classes and in this way we show that rough statistical convergence in probability is the more generalized concept compared to the usual rough statistical convergence.