Cohn,H.(1989): On the growth of multitype supercritical branching processes in a random environment, Annals of Probability, No. 3, 1118-1123.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....critical and subcritical according as ElnOE 0 0 (1) or 0. Limit theorems for supercriticl branching processses in random environments have ben investigated by Athreya and Karlin (see [21] and [21] and Tanny (see [59] Supercritical multitype BPRE has been investigated by Cohn (see [33]) 6 Branching Random Walks The models described so far do not include any spatial component in the process. We will now describe a process that does include the spatial component. The process starts with a single initial ancestor at the origin. After one unit of time, the ancestor produces ....

Cohn,H.(1989): On the growth of multitype supercritical branching processes in a random environment, Annals of Probability, No. 3, 1118-1123.

....between different types are unbounded, which obscures at first site, the existence of scaling factor for total descendant numbers. Our approach is partly inspired by a study on multi type branching processes in random environment by Cohn. Much of our proof of Proposition 2. 1 follows the idea in [5]. In that work, a probability measure on environments is considered, and the assumptions on stationarity and ergodicity implicitly assured the last two assumptions in Proposition 2.1 (including supercriticality) to hold almost surely. This approach is not suitable for our purpose to consider ....

H. Cohn, On the growth of the multitype supercritical branching process in a random environment, Ann. Probab. 17 (1989) 1118--1123.

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