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The first exit of almost strongly recurrent semi-Markov processes

Joachim Domsta, Franciszek Grabski (1995)

Applicationes Mathematicae

Let ( · ) , n ∈ N, be a sequence of homogeneous semi-Markov processes (HSMP) on a countable set K, all with the same initial p.d. concentrated on a non-empty proper subset J. The subrenewal kernels which are restrictions of the corresponding renewal kernels on K×K to J×J are assumed to be suitably convergent to a renewal kernel P (on J×J). The HSMP on J corresponding to P is assumed to be strongly recurrent. Let [ π j ; j ∈ J] be the stationary p.d. of the embedded Markov chain. In terms of the averaged...

The scaling limits of a heavy tailed Markov renewal process

Julien Sohier (2013)

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

In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the α -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 , ∞ ) × [ 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.

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