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.
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