. K.B. ATHREYA, S. KARLIN, On branching processes with random environments, I: extinction probabilities. Ann. Math. Statist., 42 (1971), 1499-1520. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Branching Processes - Athreya, Vidyashankar (1999) (113 citations) Self-citation (Athreya) (Correct)
.... ) 5.2) where 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 ....
....= 1) 1 if and only if E(lnOE 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 ....
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Athreya,K.B. and Karlin, S.(1971): On branching processes with random environments, II-Limit Theorems, Annals of Mathematical Statistics, 42, 1843-1858.
Branching Processes - Athreya, Vidyashankar (1999) (113 citations) Self-citation (Athreya) (Correct)
.... 0 (q(T ) 5.2) where 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) ....
Athreya,K.B. and Karlin, S.(1971): On branching processes with random environments, I-Extinction Probabilities, Annals of Mathematical Statistics, 42, 1499-1520.
Unknown - (2002) (Correct)
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. K.B. ATHREYA, S. KARLIN, On branching processes with random environments, I: extinction probabilities. Ann. Math. Statist., 42 (1971), 1499-1520.
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