A general law of precise asymptotics for the counting process of record times

This paper achieves a general law of precise asymptotics for the counting process of record times of i.i.d. absolutely continuous random variables. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in studies of complete convergence. This extends and generalizes the corresponding results in Stochastic Process. Appl. 101 (2002) 233-239.