Distribution of the Particles of a Critical Branching Wiener Process

Consider a critical branching Wiener process in Rd. Let {FT(x),T=1,2,... ,x∈ Rd} be the distribution of the particles living at time T. The main result of this paper tells us that any given absolutely continuous function F(x) will be well approximated by FT(x) with positive probability if T is big e...

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Bibliographic Details
Published in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 1996-03, Vol.2 (1), p.63-80
Main Author: Révész, Pál
Format: Article
Language:English
Subjects:
Random variables
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Summary:Consider a critical branching Wiener process in Rd. Let {FT(x),T=1,2,... ,x∈ Rd} be the distribution of the particles living at time T. The main result of this paper tells us that any given absolutely continuous function F(x) will be well approximated by FT(x) with positive probability if T is big enough and the process does not die out up to T.
ISSN:1350-7265
DOI:10.2307/3318569