CHARACTERIZATION PROBLEM OF SUPERPOSITION OF TWO RENEWAL PROCESSES

N₁（t）,N₂（t） are two independent renewal processes. If N（t）=N₁（t）+N₂（t） is also a renewal process and the interval times of N₁（t）,N₂（t） belong to NBUE（NWUE）, we show that N₁（t）,N₂（t）, N（t） must be Poisson processes. We also improve the conclusions in Karlin’s book. Similar conclusions are obtained about the superposition of two renewal processes with delayed and looked times.