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A weighted occupation time for a class of measured-valued branching processes
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  • Published: January 1986

A weighted occupation time for a class of measured-valued branching processes

  • I. Iscoe1 

Probability Theory and Related Fields volume 71, pages 85–116 (1986)Cite this article

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Summary

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→∞. 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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Ottawa, KIN 6N5, Ottawa, Canada

    I. Iscoe

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  1. I. Iscoe
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Research supported in part by Natural Sciences and Engineering Research Council of Canada

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Cite this article

Iscoe, I. A weighted occupation time for a class of measured-valued branching processes. Probab. Th. Rel. Fields 71, 85–116 (1986). https://doi.org/10.1007/BF00366274

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  • Received: 15 August 1981

  • Revised: 19 March 1984

  • Accepted: 06 May 1985

  • Issue Date: January 1986

  • DOI: https://doi.org/10.1007/BF00366274

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Keywords

  • Stochastic Process
  • Probability Theory
  • Random Field
  • Mathematical Biology
  • Central Limit
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