arXiv subjects

Loic Chaumont

Publications and source records attributed to Loic Chaumont.

2 recordsLinked to original sources

arXiv2007

Some explicit identities associated with positive self-similar Markov processes

We consider some special classes of Lévy processes with no gaussian component whose Lévy measure is of the type $π(dx)=e^{γx}ν(e^x-1) dx$, where $ν$ is the density of the stable Lévy measure and $γ$ is a positive parameter which depends on its characteristics. These processes were introduced in \cite{CC} as the underlying Lévy processes in the Lamperti representation of conditioned stable Lévy processes. In this paper, we compute explicitly the law of these Lévy processes at their first exit time from a finite or semi-finite interval, the law of their exponential functional and the first hitting time probability of a pair of points.

math.PR↗

arXiv2007

On the genealogy on conditioned stable Lévy forest

We give a realization of the stable Lévy forest of a given size conditioned by its mass from the path of the unconditioned forest. Then, we prove an invariance principle for this conditioned forest by considering $k$ independent Galton-Watson trees whose offspring distribution is in the domain of attraction of any stable law conditioned on their total progeny to be equal to $n$. We prove that when $n$ and $k$ tend towards $+\infty$, under suitable rescaling, the associated coding random walk, the contour and height processes converge in law on the Skorokhod space respectively towards the "first passage bridge" of a stable Lévy process with no negative jumps and its height process.

math.PR↗