arXiv subjects

Guillaume Voisin

Publications and source records attributed to Guillaume Voisin.

21 records · Page 2Linked to original sources

arXiv2010

Local time of a diffusion in a stable Lévy environment

We consider a one-dimensional diffusion in a stable Lévy environment. We show that the normalized local time process refocused at the bottom of the standard valley with height $\log t$, $(L_X(t,\mathfrak m_{\log t}+x)/t,x\in \R)$, converges in law to a functional of two independent Lévy processes conditioned to stay positive. To prove this result, we show that the law of the standard valley is close to a two-sided Lévy process conditioned to stay positive. We also obtain the limit law of the supremum of the normalized local time. This result has been obtained by Andreoletti and Diel in the case of a Brownian environment.

math.PR↗

arXiv2010

Pruning a Lévy continuum random tree

Given a general critical or sub-critical branching mechanism, we define a pruning procedure of the associated Lévy continuum random tree. This pruning procedure is defined by adding some marks on the tree, using Lévy snake techniques. We then prove that the resulting sub-tree after pruning is still a Lévy continuum random tree. This last result is proved using the exploration process that codes the CRT, a special Markov property and martingale problems for exploration processes. We finally give the joint law under the excursion measure of the lengths of the excursions of the initial exploration process and the pruned one.

math.PR↗

arXiv2010

Dislocation measure of the fragmentation of a general Lévy tree

Given a general critical or sub-critical branching mechanism and its associated Lévy continuum random tree, we consider a pruning procedure on this tree using a Poisson snake. It defines a fragmentation process on the tree. We compute the family of dislocation measures associated with this fragmentation. This work generalizes the work made for a Brownian tree [Abraham, Serlet] and for a tree without Brownian part [Abraham, Delmas].

math.PR↗