Probability Theory and Related Fields

, Volume 71, Issue 1, pp 85–116

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

  • I. Iscoe
Article

DOI: 10.1007/BF00366274

Cite this article as:
Iscoe, I. Probab. Th. Rel. Fields (1986) 71: 85. doi:10.1007/BF00366274

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 Rd. 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.

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • I. Iscoe
    • 1
  1. 1.Department of MathematicsUniversity of OttawaOttawaCanada