Caratheodory approximate solutions for a class of stochastic differential equations involving the local time at point zero with one-sided Lipschitz continuous drift coefficients

In this paper, we study the Caratheodory approximate solution for a class of stochastic differential equations involving the local time at point zero. Based on the Caratheodory approximation procedure, we prove that stochastic differential equations involving the local time at point zero have a unique solution, and we show that the Caratheodory approximate solution converges to the solution of stochastic differential equations involving the local time at point zero with one-sided Lipschitz drift coefficient.