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The weak convergence of regenerative processes using some excursion path decompositions

Amaury Lambert;  Florian Simatos — 2014

Annales de l'I.H.P. Probabilités et statistiques

We consider regenerative processes with values in some general Polish space. We define their ε -big excursions as excursions e such that ϕ ( e ) g t ; ε , where ϕ is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of e . We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of ε -big excursions and of their endpoints, for all ε in a set whose closure contains 0 . Finally, we provide...

Adaptive dynamics in logistic branching populations

Nicolas Champagnat;  Amaury Lambert — 2008

Banach Center Publications

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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