Une application de la théorie des excursions à une diffusion réfléchie dégénérée. (An application of the theory of excursions to a degenerated reflected diffusion)
We consider the \(R^ 2\)-valued reflected stochastic differential equation associated with the degenerated differential operator \[ (1/2)\partial^ 2/\partial x^ 2+x \partial /\partial y. \] We study the excursion phenomenon around the point (0,0). We are able to identify the law of the inverse of the local time as a stable subordinator with order 1/4 and to give for it an occupation time formula. These facts enable us to study the behavior of the law of the process near the point (0,0) and to refine, in our case, results obtained by P. Krée (1985) by means of analytical methods.
scientific article; zbMATH DE number 4137122
scientific article