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Limit theorems for strongly and intermediately supercritical branching processes in random environment with linear fractional offspring distributions

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  • Böinghoff, Christian

Abstract

In the present paper, we characterize the behavior of supercritical branching processes in random environment with linear fractional offspring distributions, conditioned on having small, but positive values at some large generation. As it has been noticed in previous works, there is a phase transition in the behavior of the process. Here, we examine the strongly and intermediately supercritical regimes The main result is a conditional limit theorem for the rescaled associated random walk in the intermediately case.

Suggested Citation

  • Böinghoff, Christian, 2014. "Limit theorems for strongly and intermediately supercritical branching processes in random environment with linear fractional offspring distributions," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3553-3577.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:11:p:3553-3577
    DOI: 10.1016/j.spa.2014.05.009
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    References listed on IDEAS

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    1. Nakashima, Makoto, 2013. "Lower deviations of branching processes in random environment with geometrical offspring distributions," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3560-3587.
    2. Afanasyev, V.I. & Geiger, J. & Kersting, G. & Vatutin, V.A., 2005. "Functional limit theorems for strongly subcritical branching processes in random environment," Stochastic Processes and their Applications, Elsevier, vol. 115(10), pages 1658-1676, October.
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