Abstract
This paper develops almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces, we obtain Chung type SLLN and the Jaite type SLLN for sequences of negatively superadditive dependent random vectors in Hilbert spaces. Rate of convergence is studied through considering almost sure convergence to 0 of tail series. As an application, the almost sure convergence of degenerate von Mises-statistics is investigated.
Acknowledgments
The authors would like to express their deep thanks to anonymous referees for their useful comments. This work was supported by the Vietnam National University, Hanoi (grant no. QG.16.09) and Funds for Science and Technology Development of the University of Da Nang (grant no. B2018 - DN03 - 27).