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Limit Processes for Age-Dependent Branching Particle Systems

Author

Listed:
  • I. Kaj

    (Uppsala University)

  • S. Sagitov

    (Institute of Theoretical and Applied Mathematics, NAS of Kazakhstan)

Abstract

We consider systems of spatially distributed branching particles in R d . The particle lifelengths are of general form, hence the time propagation of the system is typically not Markov. A natural time-space-mass scaling is applied to a sequence of particle systems and we derive limit results for the corresponding sequence of measure-valued processes. The limit is identified as the projection on R d of a superprocess in R +×R d . The additive functional characterizing the superprocess is the scaling limit of certain point processes, which count generations along a line of descent for the branching particles.

Suggested Citation

  • I. Kaj & S. Sagitov, 1998. "Limit Processes for Age-Dependent Branching Particle Systems," Journal of Theoretical Probability, Springer, vol. 11(1), pages 225-257, January.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:1:d:10.1023_a:1021607311191
    DOI: 10.1023/A:1021607311191
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    References listed on IDEAS

    as
    1. Sagitov, Serik, 1994. "Measure-branching renewal processes," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 293-307, August.
    2. Dawson, Donald A. & Fleischmann, Klaus, 1988. "Strong clumping of critical space-time branching models in subcritical dimensions," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 193-208, December.
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