We consider a generalized inhomogeneous continuous time renewal equation on the halfline, that is the Volterra integral equation with a nonnegative bounded (or substochastic) kernel. It is assumed that this kernel on the large time scale can be approximated by a convolution kernel, generated by a stochastic distribution. Under some asymptotic conditions on the perturbation we find the improved conditions of boundness, under which is proved the existence of limits and the numerical estimations of the stability of the solution of the perturbed equation. Some applications are considered.
