Hautphenne, S.Latouche, G.Nguyen, G.Latouche, G.Ramaswami, V.Sethuraman, J.Sigman, K.Squillante, M.Yao, D.2014-10-272014-10-272013Springer Proceedings in Mathematics and Statistics, 2013 / Latouche, G., Ramaswami, V., Sethuraman, J., Sigman, K., Squillante, M., Yao, D. (ed./s), vol.27, pp.87-106146144909X97814614490962194-10092194-1017http://hdl.handle.net/2440/86702We consider multitype Markovian branching processes subject to catastrophes which kill random numbers of living individuals at random epochs. It is well known that the criteria for the 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 where 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 individual. The upper bound appears to be often much tighter than the lower bound.en© Springer Science+Business Media New York 2013Branching processes; matrix-analytic methods; catastrophes; extinction criteria; Lyapunov exponentConference paper003001111710.1007/978-1-4614-4909-6_52-s2.0-84883343666102175