The joint law of ages and residual lifetimes for two schemes of nested regenerative sets.
Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct.
Proof(s) of the Lamperti representation of continuous-state branching processes.
The weak convergence of regenerative processes using some excursion path decompositions
We consider regenerative processes with values in some general Polish space. We define their -big excursions as excursions such that , where is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of . We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of -big excursions and of their endpoints, for all in a set whose closure contains . Finally, we provide...
Adaptive dynamics in logistic branching populations
The biological theory of adaptive dynamics proposes a description of the long-time evolution of an asexual population, based on the assumptions of large population, rare mutations and small mutation steps. Under these assumptions, the evolution of a quantitative dominant trait in an isolated population is described by a deterministic differential equation called 'canonical equation of adaptive dynamics'. In this work, in order to include the effect of genetic drift in this model, we consider instead...
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