期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2017
卷号：XIV
页码：381-402
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：The reproduction speed of a continuous-time branching random walk isproportional to a positive parameter . There is a threshold for , which is calledw, that separates almost sure global extinction from global survival. Analogously,there exists another threshold s below which any site is visited almost surelya finite number of times (i.e. local extinction) while above it there is a positiveprobability of visiting every site infinitely many times. The local critical parameters is completely understood and can be computed as a function of the reproductionrates. On the other hand, only for some classes of branching random walks it isknown that the global critical parameter w is the inverse of a certain function ofthe reproduction rates, which we denote by Kw. We provide here new sufficientconditions which guarantee that the global critical parameter equals 1/Kw. Thisresult extends previously known results for branching random walks on multigraphsand general branching random walks. We show that these sufficient conditions aresatisfied by periodic tree-like branching random walks. We also discuss the criticalparameter and the critical behaviour of continuous-time branching processes invarying environment. So far, only examples where w = 1/Kw were known; herewe provide an example where w > 1/Kw.
关键词：branching random walk; branching process; local survival; global;survival; varying environment; tree-like; critical parameters; generating function.
