A new discretization scheme for one dimensional stochastic differential equations using time change method

We propose a new numerical method for one dimensional stochastic differential equations (SDEs). The main idea of this is based on representation weak solution an SDE using time-changed Brownian motion, which dates back to Doeblin (1940). In cases where the diffusion coefficient bounded and β-Holder continuous with 0<β≤1, we provide rate strong convergence. An advantage our approach that approximate solution, enables us treat SDEs no solution. Our scheme first achieve convergence case 0<β<1∕2.