Limit Processes for Age-Dependent Branching Particle Systems |
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Authors: | I Kaj S Sagitov |
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Institution: | (1) Department of Mathematics, Uppsala University, Box 480, S-751 06 Uppala, Sweden;(2) Institute of Theoretical and Applied Mathematics, NAS of Kazakhstan, Almaty, Kazakhstan |
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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. |
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Keywords: | Superprocess age-dependent branching Markov renewal process Lé vy process |
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