Pairs of renewal processes whose superposition is a renewal process (Q1411886)

Necessary and sufficient conditions for the superposition of two independent renewal processes to be a renewal process are completed. The case of renewal processes with strictly positive inter-renewal times goes back to \textit{S. M.\ Samuels} [J.\ Appl.\ Probab.\ 11, 72-85 (1974; Zbl 0276.60083)] and leads to Poisson processes. The new cases are exhausted by binomial-like processes, one of them possibly degenerated, sitting on scaled nonnegative integers.