Limit Processes for Age-Dependent Branching Particle Systems

I. Kaj and S. Sagitov
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I. Kaj: Uppsala University
S. Sagitov: Institute of Theoretical and Applied Mathematics, NAS of Kazakhstan

Journal of Theoretical Probability, 1998, vol. 11, issue 1, 225-257

Abstract: 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.

Keywords: Superprocess; age-dependent branching; Markov renewal process; Lévy process (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1021607311191

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