Abstract:In this paper, we consider the laws of large numbers with infinite means
based on ?-mixing sequences. An exact weak law and a strong law are obtained
for ?-mixing asymmetrical Cauchy random variables. It is also presented that
the weak law cannot extend to a strong law. In addition, some simulations
are presented to illustrate our results of the laws of large numbers.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.