Scaling limits of a heavy tailed Markov renewal process.

Julien Sohier (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the $\ga$-stable regenerative set. We then apply these results to the strip wetting model which is a random walk $S$ constrained above a wall and rewarded or penalized when it hits the strip $[0,\infty) \times [0,a]$ where $a$ is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.

Mots clés: Regenerative sets.; Heavy tailed Markov renewals; Scaling limits; Random walks conditioned to stay positive; Regenerative sets

Domaines: Probabilités [math.PR]

Julien Sohier. Scaling limits of a heavy tailed Markov renewal process.. 2011. ⟨hal-00593642v2⟩