两个更新过程叠加的特征问题

CHARACTERIZATION PROBLEM OF SUPERPOSITION OF TWO RENEWAL PROCESSES

N_1(t),N_2(t)是两个独立更新过程,如N(t)=N_1(t)+N_2(t)仍是一更新过程,本文证明了当N_1(t),N_2(t)的间隔分布属于NBUE(NWUE)分布类时,N_1(t),N_2(t),N(t)都是Poisson过程,并改进了Karlin书中的结论。在§2中对更广的具有延迟和镇住时间的两更新过程的叠加问题得到了类似的结论。

N_1(t), N_2(t) are two independent renewal processes. If N(t)=N_1(t)+N_2(t) is also a renewal process and the interval times of N_1(t), N_2(t) belong to NBUE(NWUE), we show that N_1(t), N_2(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.