Caratheodory approximate solutions for a class of perturbed stochastic differential equations with reflecting boundary

In this work, we study the Caratheodory approximate solution for a class of one-dimensional perturbed stochastic differential equations with reflecting boundary (PSDERB). Based on the Caratheodory approximation procedure, we prove that PSDERB have a unique solution and show that the Caratheodory approximate solution converges to the solution of PSDERB whose both drift and diffusion coefficients are non-Lipschitz. After that, we establish an explicit rate of convergence in the case of PSDERB with Lipschitz coefficients.