Volterra equation of convolution type

Summary

A Volterra equation of convolution type is a Volterra integral equation whose kernel depends only on the difference $t - s$. Its integral term is the convolution $\int_0^t k(t - s) \, x(s) \, ds$ on the half-line. Such equations describe systems whose rules do not change in time, and the Laplace transform turns them into algebraic equations. Renewal equations, Abel's equation and many models with memory are of this type.