PROBABILISTIC REPRESENTATION FOR SOLUTIONS OF A POROUS MEDIA TYPE EQUATION WITH NEUMANN BOUNDARY CONDITION: THE CASE OF THE HALF-LINE

摘要

The purpose of this paper consists of proposing a generalized solution for a porous media type equation on a half-line with Neumann boundary condition and prove a probabilistic representation of this solution in terms of an associated microscopic di usion. The main idea is to construct a stochastic di erential equation with re ection, which has a solution in law and whose marginal law densities provide the unique solution of the porous media type equation.