arXiv subjects

Elie Cerf

Publications and source records attributed to Elie Cerf.

2 recordsLinked to original sources

arXiv2024

Computing the Yaglom limit of Markov chains with a single exit state using their excursion measure

We prove in this article the existence of the Yaglom limit for Markov chains on discrete state spaces in the setting where the absorbing state is accessible from a single non-absorbing state. We use a representation of the trajectories of this process by its excursion away from death, that allows us to link the Yaglom limit with the large deviations behaviour of the inverse of its local time at the exit state, and to compute its minimal quasi-stationary distribution with its excursion measure.

math.PR↗

arXiv2023

The minimal quasi-stationary distribution of the absorbed M/M/$\infty$ queue

We give in this paper two characterizations of the minimal exponential rate of survival $θ$ * of the M/M/$\infty$ queue. The first one is a derivation of a known result on the duration of excursions of this process. The second one was conjectured by Mart{í}nez and Ycart [8] and is proved using complex analysis by establishing a connection with the first characterization in terms of the incomplete gamma function.

math.PR↗