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A weighted occupation time for a class of measure-valued branching processes. (English) Zbl 0555.60034
A weighted occupation time is defined for measure-valued processes and a representation for it is obtained for a class of measure-valued branching random motions on \(R^ d\). Considered as a process in its own right, the first and second order asymptotics are found as time \(t\to \infty\). Specifically the finiteness of the total weighted occupation time is determined as a function of the dimension d, and when infinite, a central limit type renormalization is considered, yielding Gaussian or asymmetric stable generalized random fields in the limit. In one Gaussian case the results are contrasted in high versus low dimensions.

MSC:
60G60 Random fields
60G50 Sums of independent random variables; random walks
60J55 Local time and additive functionals
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