On the complete convergence for uncertain random variables

In some complex systems, the randomness and uncertainty phenomena may arise simultaneously, which inspires us to develop the uncertain random variable in chance space. Based on the chance theory, we propose the concept of complete convergence and investigate the relations among the existing common types of convergence including convergence almost surely, convergence in measure, convergence in distribution and convergence in mean. All of the relations are illustrated via the corresponding examples or counterexamples. Additionally, we give an equivalent condition and a sufficient condition of convergence completely for uncertain random variables and provide an example to explain the conditions.