Critical multitype branching processes in a random environment. (English. Russian original) Zbl 1282.60086
Discrete Math. Appl. 17, No. 6, 587-606 (2007); translation from Diskretn. Mat. 19, No. 4, 23-41 (2007).
Summary: We investigate a multitype Galton-Watson process in a random environment generated by a sequence of independent identically distributed random variables. Assuming that the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices satisfies Spitzer’s condition, we find the asymptotics of the survival probability at time \(n\) as \(n\to\infty\).
MSC:
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 60G50 | Sums of independent random variables; random walks |
| 60K37 | Processes in random environments |
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