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Branching random walks I

Author

Listed:
  • Asmussen, Soren
  • Kaplan, Norman

Abstract

A general method is developed with which various theorems on the mean square convergence of functionals of branching random walks are proven. The results cover extensions and generalizations of classical central limit analogues as well as a result of a different type.

Suggested Citation

  • Asmussen, Soren & Kaplan, Norman, 1976. "Branching random walks I," Stochastic Processes and their Applications, Elsevier, vol. 4(1), pages 1-13, January.
    • Handle: RePEc:eee:spapps:v:4:y:1976:i:1:p:1-13
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    Citations

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    Cited by:

    1. Gao, Zhiqiang & Liu, Quansheng, 2016. "Exact convergence rates in central limit theorems for a branching random walk with a random environment in time," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2634-2664.
    2. 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).
    3. Gao, Zhi-Qiang, 2019. "Exact convergence rate in the local central limit theorem for a lattice branching random walk on Zd," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 58-66.
    4. Durrett, R. & Lanchier, N., 2008. "Coexistence in host-pathogen systems," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1004-1021, June.
    5. Xiaoqiang Wang & Chunmao Huang, 2017. "Convergence of Martingale and Moderate Deviations for a Branching Random Walk with a Random Environment in Time," Journal of Theoretical Probability, Springer, vol. 30(3), pages 961-995, September.
    6. Shi, Wanlin, 2019. "A note on large deviation probabilities for empirical distribution of branching random walks," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 18-28.
    7. Haojie Hou & Yan-Xia Ren & Renming Song, 2024. "Asymptotic Expansions for Additive Measures of Branching Brownian Motions," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3355-3394, November.
    8. Gao, Zhiqiang, 2017. "Exact convergence rate of the local limit theorem for branching random walks on the integer lattice," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1282-1296.
    9. Borovkov, K. & Motyer, A., 2005. "On the asymptotic behaviour of a simple growing point process model," Statistics & Probability Letters, Elsevier, vol. 72(3), pages 265-275, May.
    10. Gao, Zhi-Qiang, 2018. "A second order asymptotic expansion in the local limit theorem for a simple branching random walk in Zd," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4000-4017.

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