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Asymptotic expansions in the local limit theorem for a branching Wiener process

Author

Listed:
  • Deng, Guantie
  • Fan, Xiequan
  • Gao, Zhi-Qiang

Abstract

Consider a supercritical branching Wiener process in Rd. Let Zn(A) be the number of the nth generation particles located in a given set A⊂Rd. Under the moment condition of EX(lnX)1+λ type, the complete asymptotic expansions of Zn(A) as n tends to infinity are obtained. This result gives an alternative version of the work by Révész, Rosen and Shi (2005), hence generalizing theirs by weakening the second moment condition therein.

Suggested Citation

  • Deng, Guantie & Fan, Xiequan & Gao, Zhi-Qiang, 2023. "Asymptotic expansions in the local limit theorem for a branching Wiener process," Statistics & Probability Letters, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:stapro:v:199:y:2023:i:c:s0167715223000809
    DOI: 10.1016/j.spl.2023.109856
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    References listed on IDEAS

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    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.
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