报告题目：Markovian binary trees in a random environment: extinction criteria
Markovian binary trees are a special class of branching processes, for which the individuals have a phase-type lifetime and a phase-type number of offsprings. We show how the Markovian structure is used to derive interesting characteristics. Next, we assume that such branching processes are subject to catastrophes which occur at random epochs and kill random numbers of living individuals. It is well known that the criteria for extinction of such a process is related to the conditional growth rate of the population, given the history of the process of catastrophes, and that it is usually hard to evaluate.
We give a simple characterization in the case when all individuals have the same probability of surviving a catastrophe, and we determine upper and lower bounds in the case where survival depends on the type of the individual. The upper bound appears to be often much tighter than the lower bound.