Abstract
In this work, we study the Carathéodory approximate solution for a class of one-dimensional perturbed stochastic differential equations with reflecting boundary (PSDERB). Based on the Carathéodory approximation procedure, we prove that PSDERB have a unique solution and show that the Carathéodory 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.
Acknowledgements
We are thankful to the editor and the anonymous referee for very careful reading, and her/his valuable remarks and suggestions which led to improvement of the paper.