A two-dimensional oblique extension of Bessel processes
Résumé
Starting from a process in the nonnegative quadrant whose components are independent Bessel processes, an additional drift of the same kind is added to each component which depends on the other component. Strong existence and uniqueness are obtained for a large set of parameters. The question of hitting the corner is the source of main difficulties. Some properties of the usual one-dimensional Bessel processes are preserved. The results are reminiscent of the study of a Brownian motion with oblique reflection in the quadrant. Actually, the same skew symmetry condition is involved when looking for a stationary distribution in product form when adding a constant drift. The terms of the product are now gamma distributions in place of exponential ones.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)