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Compound Poisson population models are particular conditional branching process models. A formula for the transition probabilities of the backward process for general compound Poisson models is verified. Symmetric compound Poisson models are defined in terms of a parameter θ ∈ (0, ∞) and a power series φ with positive radius r of convergence. It is shown… (More)

- Martin Möhle, Helmut Pitters
- 2014

A spectral decomposition for the generator and the transition probabilities of the block counting process of the Bolthausen–Sznitman coalescent is derived. This decomposition is closely related to the Stirling numbers of the first and second kind. The proof is based on generating functions and exploits a certain factorization property of the… (More)

We study the asymptotics of the extended Moran model as the total population size N tends to infinity. Two convergence results are provided, the first result leading to discrete-time limiting coalescent processes and the second result leading to continuous-time limiting coalescent processes. The limiting coalescent processes allow for multiple mergers of… (More)

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