Christophe Profeta

We consider a one-dimensional stable Langevin process confined in the upper half-plane and submitted to a diffusive-reflective boundary condition whenever the particle position hits 0. We show that different regimes appear according to the value of the chosen parameters. We then use this study to construct the law of a (free) stable Langevin process conditioned to stay positive, thus extending earlier works on the integrated Brownian motion. Such construction finally enables us to improve some recent persistence probability estimates. This is a joint work with Jean-François Jabir.
Departamento de Matemáticas

Pontificia Universidad Católica de Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Centro de Modelamiento Matemático (CMM)

Facultad de Ciencias Físicas y Matemáticas (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile