On coupling of renewal processes with use of failure rates
Besides the classical tools for renewal processes coupling methods proved to be successful. Especially asymptotic results for renewal processes are shown by coupling the process to a stationary renewal process, which is easier to handle. \textit{M. Brown} [Ann. Probab. 8, 227-240 (1980; Zbl 0429.60084)] considered monotonicity properties for renewal processes like decreasing (increasing) failure rates of the lifetime distribution. In this paper the author introduces an appropriate coupling for renewal processes and shows, that most of Brown's results can be deduced from coupling methods, for example sharp lower bounds for the renewal function. Additionally he obtains rates of convergence toward stationarity.
failure rates of the lifetime distribution
scientific article; zbMATH DE number 3988424