Distributions of lifetime after explosion for birth and death processes (Q1267227)

If a birth and death process in which explosion can take place but the process may continue thereafter (namely, one which is not the minimal process associated with its generator), the behaviour of the process following the first explosion is considered. The distribution and mean of the residual lifespan and the probability that this residual lifespan is zero are found explicitly in terms of the parameters defining the process. Use is made of the fact that the post-explosion process is independent of the pre-explosion process, and distributional results are expressed in terms of Laplace transforms.