Tanny,D.(1977): Limit theorems for branching processes in random environment, Annals of Probability, No. 1, 100-116.  Home/Search   Document Not in Database   Summary   Related Articles

....OE 0 ( Delta) is the probability generating function of the probability distribution 0 and T is the shifted environmental sequence f i g 1 1 . If the sequence is stationary and ergodic then it can be shown that P (q( 1) is zero or one (see Athreya and Karlin [20] 21] and Tanny [59]) The criterion for almost sure extinction can be expressed in terms of the behavior of the conditional mean of Z n given Z 0 = 1 and . From (5.2) it follows that E(Z n 1 jZ n ; Z n OE 0 n (1) 5.3) where OE 0 n ( Delta) is the derivative of OE n ( Delta) This renders W n = Z n ....

....0 0 (1) 0: 2 The B.P.R.E. fZ n g 1 0 is called supercritical, 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 ....

Tanny,D.(1977): Limit theorems for branching processes in random environment, Annals of Probability, No. 1, 100-116.

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