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General branching processes conditioned on extinction are still branching processes

   
@article{ECP1419,
	author = {Peter Jagers and Andreas Lagerås},
	title = {General branching processes conditioned on extinction are still branching processes},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {supercritical; subcritical; extinction; multi-type branching process; general branching process; Crump-Mode-Jagers process},
	abstract = {It is well known that a simple, supercritical Bienaymé-Galton-Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where child-bearing may occur at different ages, life span may depend upon reproduction, and the whole course of events is thus affected by conditioning upon extinction.},
	pages = {no. 51, 540-547},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1419},    
        url = {http://ecp.ejpecp.org/article/view/1419}}