An approach for computing tight numerical bounds on renewal functions
This method computes tight lower & upper bounds for the renewal function. It is based on Riemann-Stieltjes integration, and provides bounds for solving certain renewal equations used in the study of availability. An error analysis is given for the numerical bounds when inter-renewal time distributions are sufficiently smooth. Three examples are explored that demonstrate the accuracy of these computed numerical bounds.
renewal function riemann-stieltjes integral renewal equation