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Minimal Position of Branching Random Walks in Random Environment

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  • Makoto Nakashima

    (Kyoto University)

Abstract

We consider branching random walks in random environment (BRWRE) on ℕ with only one particle starting at the origin. Particles reproduce according to offspring distribution (which depends on its locations) and move one step to the right (with a probability in (0,1] which may depend on the location) or stay in the same site. We give an estimate to the minimal displacement of BRWRE at time n in the case where the essential supremum of mean number of offsprings which stay in the same place is equal to 1.

Suggested Citation

  • Makoto Nakashima, 2013. "Minimal Position of Branching Random Walks in Random Environment," Journal of Theoretical Probability, Springer, vol. 26(4), pages 1181-1217, December.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:4:d:10.1007_s10959-012-0410-y
    DOI: 10.1007/s10959-012-0410-y
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    References listed on IDEAS

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    1. Nina Gantert & Sebastian Müller & Serguei Popov & Marina Vachkovskaia, 2010. "Survival of Branching Random Walks in Random Environment," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1002-1014, December.
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    Cited by:

    1. Huang, Chunmao & Liu, Quansheng, 2024. "Limit theorems for a branching random walk in a random or varying environment," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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