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Survival of branching random walks with absorption

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  • Aïdékon, Elie
  • Jaffuel, Bruno

Abstract

We consider a branching random walk on starting from x>=0 and with a killing barrier at 0. At each step, particles give birth to b children, which move independently. Particles that enter the negative half-line are killed. In the case of almost sure extinction, we find asymptotics for the survival probability at time n, when n tends to infinity.

Suggested Citation

  • Aïdékon, Elie & Jaffuel, Bruno, 2011. "Survival of branching random walks with absorption," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 1901-1937, September.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:9:p:1901-1937
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    References listed on IDEAS

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    1. Kesten, Harry, 1978. "Branching brownian motion with absorption," Stochastic Processes and their Applications, Elsevier, vol. 7(1), pages 9-47, March.
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    Cited by:

    1. Mallein, Bastien, 2015. "Maximal displacement of a branching random walk in time-inhomogeneous environment," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3958-4019.
    2. Madaule, Thomas, 2016. "First order transition for the branching random walk at the critical parameter," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 470-502.

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