An asymptotic solution of the integral equation for the second moment function in geometric processes

摘要

In this study, we derive an asymptotic solution of the integral equation satisfied by the second moment function . We first find the Laplace transform and then obtain asymptotically by inversion. Further, we have derived the asymptotic expressions of for some special lifetime distributions such as exponential, gamma, Weibull, lognormal and truncated normal. Finally, the asymptotic solution is compared with the numerical solution to evaluate its performance.