30 citations · 89 across the 22 of their papers we have counts for
5 papers · 1 filter
Consistency of the maximum likelihood estimate for Non-homogeneous Markov-switching models
Pierre Ailliot, Francoise Pene
Many nonlinear time series models have been proposed in the last decades. Among them, the models with regime switchings provide a class of versatile and interpretable models which…
Self-intersections of trajectories of Lorentz process
Francoise Pene
We study the asymptotic behaviour of the number of self-intersections of a trajectory of a periodic planar Lorentz process with strictly convex obstacles and finite horizon. We giv…
On caustics by reflection of algebraic surfaces
Alfrederic Josse, Francoise Pene
Given a point S (the light position) in P^3 and an algebraic surface Z (the mirror) of P^3, the caustic by reflection of Z from S is the Zariski closure of the envelope of the refl…
An asymptotic estimate of the variance of the self-intersections of a planar periodic Lorentz process
Francoise Pene
We consider a periodic planar Lorentz process with strictly convex obstacles and finite horizon. This process describes the displacement of a particle moving in the plane with unit…
Degree and class of caustics by reflection for a generic source
Alfrederic Josse, Francoise Pene
We are interested in the study of caustics by reflection of irreducible algebraic planar curves (in the complex projective plane). We prove the birationality of the caustic map (fo…