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We consider a generalized inhomogeneous continuous-time renewal equation on the semiaxis that reduces to the Volterra integral equation with a nonnegative bounded (or substochastic) kernel. It is assumed that the kernel can be approximated in a large time scale by a convolution kernel generated by a stochastic distribution. Under some asymptotic assumptions imposed on the perturbation we find an improved condition for the boundedness; the latter condition is used to prove the existence of the limit of a solution of the perturbed equation and to establish estimates for the deviation from a solution of a nonperturbed equation. Some examples are discussed.

Improvement of the stability of solutions of an inhomogeneous perturbed renewal equation on the semiaxis