It is well-known that the complete convergence theorem for i.i.d, random vari- ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4] obtained a moment version of Hsu and Robbins se...It is well-known that the complete convergence theorem for i.i.d, random vari- ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4] obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever c goes to zero, so it is of interest to investigate the asymptotic behavior of the series as e goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.展开更多
In this paper, we present a local Csorgo- Revesz type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Levy's modulus of contin...In this paper, we present a local Csorgo- Revesz type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Levy's modulus of continuity for Brownian motion.展开更多
基金supported by National Natural Science Foundation of China(11171303,61273093)the Specialized Research Fund for the Doctor Program of Higher Education(20090101110020)
文摘It is well-known that the complete convergence theorem for i.i.d, random vari- ables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4] obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever c goes to zero, so it is of interest to investigate the asymptotic behavior of the series as e goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.
基金Supported by NSFC(Grant Nos.11571262 and 11661025)Science Research Foundation of Guangxi Education Department(Grant No.YB2014117)
文摘In this paper, we present a local Csorgo- Revesz type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Levy's modulus of continuity for Brownian motion.