| 1. |
- Jagers, Peter, 1941, et al.
(författare)
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General branching processes conditioned on extinction are still branching processes
- 2008
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Ingår i: Electronic Communications in Probability. - 1083-589X. ; 13, s. 540-547
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Tidskriftsartikel (refereegranskat)abstract
- It is well known that a simple, supercritical Bienaymé-Galton-Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where child-bearing may occur at different ages, life span may depend upon reproduction, and the whole course of events is thus affected by conditioning upon extinction.
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| 2. |
- Nordvall Lagerås, Andreas
(författare)
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Copulas for Markovian dependence
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Copulas have been popular to model dependence for multivariate distributions, but have not been used much in modelling temporal dependence of univariate time series. This paper shows some difficulties with using copulas even for Markov processes: some tractable copulas such as mixtures between copulas of complete co- and countermonotonicity and independence (Fréchet copulas) are shown to imply quite a restricted type of Markov process, and Archimedean copulas are shown to be incompatible with Markov chains. We also investigate Markov chains that are spreadable, or equivalently, conditionally i.i.d.
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| 3. |
- Nordvall Lagerås, Andreas, et al.
(författare)
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Reduced branching processes with very heavy tails
- 2008
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Ingår i: Journal of Applied Probability. - 0021-9002. ; 45:1, s. 190-200
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Tidskriftsartikel (refereegranskat)abstract
- The reduced Markov branching process is a stochastic model for the genealogy of an unstructured biological population. Its limit behavior in the critical case is well studied for the Zolotarev-Slack regularity parameter α∈(0,1]. We turn to the case of very heavy tailed reproduction distribution α=0 assuming Zubkov’s regularitycondition with parameter β∈(0,∞). Our main result gives a new asymptotic pattern for the reduced branching process conditioned on non-extinction during a long time interval.
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