Some results on stochastic differential equations with reflecting boundary conditions (Q702404)

The authors consider a stochastic differential equation defined on an open connected bounded subset of \(\mathbb{R}\) with reflecting boundary conditions. The main difference to earlier results is that for the drift function only a monotonicity condition of the form \((x-x',b(\omega,t,x)-b(\omega,t,x'))\leq L| x-x'| ^2\) is imposed, substituting the classical Lipschitz condition. The proof relies on the generalization of the Skorokhod problem formulation.