FURTHER RESULTS OF CONVERGENCE OF UNCERTAIN RANDOM SEQUENCES

Abstract

Convergence is an issue being widely concerned about. Thus, in this paper, we mainly put forward two types of concepts of convergence in mean and convergence in distribution for the sequence of uncertain random variables. Then some of theorems are proved to show the relations among the three convergence concepts that are convergence in mean, convergence in measure and convergence in distribution. Furthermore, several examples are given to illustrate how we use the theorems to make sure the uncertain random sequence being convergent. Finally, several counterexamples are taken to explain the relations between these different types of convergence.