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

Guantie Deng, Xiequan Fan and Zhi-Qiang Gao

Statistics & Probability Letters, 2023, vol. 199, issue C

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.

Keywords: Branching Wiener process; Local limit theorem; Asymptotic expansions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109856

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