Some properties of repeated hits after first explosion for birth and death processes

Of repeated hits and repeated explosions after first explosion for a birth and death process with explosion some properties are investigated. The properties of repeated hits after first explosion may be expressed by the properties of the first hit after the first explosion. Project supported by the National Natural Science Foundation of China (Grant No. 19761028) and the Centre of Researching Mathematics and Forstering Higher Talent, the Ministry of Education of China.