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| 2. |
- Belyaev, Yuri K, et al.
(författare)
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Weakly approaching sequences of random distributions
- 2000
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Ingår i: Journal of Applied Probability. - Umeå : Umeå universitet. - 0021-9002 .- 1475-6072.
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Rapport (refereegranskat)abstract
- We introduce the notion of weakly approaching sequences of distributions, which is a generalization of the well-known concept of weak convergence of distributions. The main difference is that the suggested notion does not demand the existence of a limit distribution. A similar definition for conditional (random) distributions is presented. Several properties of weakly approaching sequences are given. The tightness of some of them is essential. The Cramér-Lévy continuity theorem for weak convergence is generalized to weakly approaching sequences of (random) distributions. It has several applications in statistics and probability. A few examples of applications to resampling are given.
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| 3. |
- Jagers, Peter, 1941, et al.
(författare)
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Branching processes in near-critical random environments
- 2004
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 41A, s. 17-23
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Tidskriftsartikel (refereegranskat)abstract
- Branching processes are studied in random environments that are influenced by the population size and approach criticality as the population gets large. Results are applied to the polymerase chain reaction (PCR), which is empirically known to exhibit first exponential and then linear growth of molecule numbers.
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| 4. |
- Jagers, Peter, 1941, et al.
(författare)
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Branching processes with deteriorating random environments
- 2002
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Ingår i: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 39, s. 395-401
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Tidskriftsartikel (refereegranskat)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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| 8. |
- Jagers, Peter, 1941, et al.
(författare)
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Convergence to the coalescent in populations of substantially varying size.
- 2004
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Ingår i: J. Appl. Probab.. - 0021-9002. ; 41:2, s. 368-378
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Tidskriftsartikel (refereegranskat)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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| 9. |
- Janson, S
(författare)
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Moment convergence in conditional limit theorems
- 2001
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Ingår i: JOURNAL OF APPLIED PROBABILITY. - : APPLIED PROBABILITY TRUST. - 0021-9002. ; 38:2, s. 421-437
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Tidskriftsartikel (refereegranskat)abstract
- Consider a stun Sigma (N)(1) Y-i of random variables conditioned on a given value of the sum Sigma (N)(1) X-i of some other variables, where Xi and Yi are dependent but the pairs (Xi, Yi) form an i.i sequence. We consider here the case when each Xi is dis
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| 10. |
- Kaj, I, et al.
(författare)
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Coalescent theory for seed bank models
- 2001
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Ingår i: Journal of Applied Probability. - 0021-9002. ; 38:2, s. 285-300
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Tidskriftsartikel (refereegranskat)abstract
- We study the genealogical structure of samples from a population for which any given generation is made up of direct descendants from several previous generations. These occur in nature when there are seed banks or egg banks allowing an individual to leav
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