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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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##### References:
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