Renewal representation
= Renewal representation
{title2=$z=g*U$}
For positive interarrivals with law $K$, the unique locally bounded solution of $z=g+z*K$ is $z=g*U=\sum_{j\geq0}g*K^{*j}$, where $U$ is the <renewal measure>. Iteration proves the identity: the residual is bounded on each compact interval by a constant times the probability that the sum of many positive interarrivals stays in that interval, which tends to zero.