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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...

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