| 11. |
- Jagers, Peter, 1941, et al.
(author)
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Branching processes with deteriorating random environments
- 2002
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In: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 39, s. 395-401
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Journal article (peer-reviewed)abstract
- We introduce Galton-Watson style branching processes in random environments which are deteriorating rather than stationary or independent. Some primary results on process growth and extinction probability are shown. Two simple examples are given.
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| 12. |
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| 13. |
- Jagers, Peter, 1941, et al.
(author)
-
Convergence to the coalescent in populations of substantially varying size.
- 2004
-
In: J. Appl. Probab.. - 0021-9002. ; 41:2, s. 368-378
-
Journal article (peer-reviewed)abstract
- Kingman's classical coalescent uncovers the basic pattern of genealogical trees of random samples of individuals in large but time-constant populations. Time is viewed as discrete and identified with non-overlapping generations. Reproduction can be very generally taken as exchangeable (meaning that the labelling of individuals in each generation carries no significance). Recent generalisations have dealt with population sizes exhibiting given deterministic or (minor) random fluctuations. We consider population sizes which constitute a stationary Markov chain, explicitly allowing large fluctuations in short times. Convergence of the genealogical tree, as population size tends to infinity, towards the (time-scaled) coalescent is simply proved under minimal conditions. As a result, a formula for effective population size obtains, generalising the well-knownharmonic mean expression for effective size.
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| 14. |
- Jagers, Peter, 1941, et al.
(author)
-
General branching processes conditioned on extinction are still branching processes
- 2008
-
In: Electronic Communications in Probability. - 1083-589X. ; 13, s. 540-547
-
Journal article (peer-reviewed)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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| 15. |
- Jagers, Peter, 1941, et al.
(author)
-
General branching processes in discrete time as random trees.
- 2008
-
In: Bernoulli. - 1350-7265. ; 14:4, s. 949-962
-
Journal article (peer-reviewed)abstract
- The simple Galton-Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random trees, each vertex being an individual of the family tree. This viewpoint has led to new insights and a revival of classical theory. We show how a similar reinterpretation can shed new light on the more interesting forms of branching processes that allow repeated bearings and, thus, overlapping generations. In particular, we use the stable pedigree law to give a transparent description of a size-biased version of general branching processes in discrete time. This allows us to analyse the xlog x condition for exponential growth of supercritical general processes, and also the relation between simple Galton-Watson and more general branching processes.
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| 16. |
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| 17. |
- Jagers, Peter, 1941
(author)
-
Matematikens ord
- 2009
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In: LexicoNordica. ; 16, s. 315-318
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Journal article (peer-reviewed)
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| 18. |
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| 19. |
- Jagers, Peter, 1941
(author)
-
On the Complete Life Career of Populations in Environments with a Finite Carrying Capacity
- 2015
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In: Pliska Studia Mathematica. - 0204-9805. ; 24, s. 55-60
-
Journal article (peer-reviewed)abstract
- If a general branching process evolves in a habitat with a finite carrying capacity, i. e. a number such that reproduction turns subcritical as soon as population size exceeds that number, then the population may either die out quickly, or else grow up to arround the carrying capacity, where it will linger for a long time, until it starts decaying exponentially to extinction.
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| 20. |
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