Uncertain Zero-One Law and Convergence of Uncertain Sequence

A Note on Uncertain Sequence Convergence

In this paper, an uncertain version of Borel-Cantelli lemma is proved. Besides, some convergence theorems of continuous uncertain measure are proposed. Using these theorems, it is proved that the uncertainty distribution function of the uncertain integral on a real function is a normal one.

FURTHER RESULTS OF CONVERGENCE OF UNCERTAIN RANDOM SEQUENCES

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 distributio...

Convergence of complex uncertain sequences

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the convergence concepts of complex uncertain sequences: convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely. In additi...

On the convergence of uncertain sequences

On the convergence of uncertain random sequences

In this paper, a useful inequality for central moment of uncertain random variables is proved. Based on this inequality, a convergence theorem for sum of uncertain random variables is derived. A Borel–Cantelli lemma for chance measure is obtained based on the continuity assumption of uncertain measure. Finally, several convergence theorems for uncertain random sequences are established.