3 papers
math.PR2024
Asymptotic properties of the maximum likelihood estimator for Hidden Markov Models indexed by binary trees
Julien Weibel
We consider hidden Markov models indexed by a binary tree where the hidden state space is a general metric space. We study the maximum likelihood estimator (MLE) of the model param…
math.PR2024
Ergodic theorem for branching Markov chains indexed by trees with arbitrary shape
Julien Weibel
We prove an ergodic theorem for Markov chains indexed by the Ulam-Harris-Neveu tree over large subsets with arbitrary shape under two assumptions: with high probability, two vertic…
cs.DM2023
Probability-graphons: Limits of large dense weighted graphs
Romain Abraham, Jean-François Delmas, Julien Weibel
We introduce probability-graphons which are probability kernels that generalize graphons to the case of weighted graphs. Probability-graphons appear as the limit objects to study s…