Random variables are constructed for a Bellman-Harris branching process which are the extensions of backward and forward recurrence times from an ordinary renewal process. The sum of the two extended random variables is also constructed, and then the distribution functions for all three random...

Under a Bellman-Harris age-dependent branching process, a parent lives a random length of time and at death produces a random number of offspring. The parent lifetimes have the common cumulative distribution G([dot operator]) and the number of offspring per parent has a common probability...