Inhomogeneous perturbations of a renewal equation and the Cramér–Lundberg theorem for a risk process with variable premium rates
Анотація
We consider a time inhomogeneous perturbation of the classical renewal equation with continuous time that can be reduced to the integral Volterra equation with a nonnegative bounded kernel. We assume that the kernel is approximated for large time intervals by a convolution kernel generated by a probability distribution. We prove that the limit of the solution of the perturbed equation exists if the corresponding perturbation of solutions of the perturbed equation is small.
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