On the support of the solutions of stochastic differential equations

Let $x=(x(t))_{t\ge 0}$ be a solution of stochastic differential equation (1.1m) generated by a continuous semimartingale and let $x^\omega=(x^\omega(t))_{t\ge 0}$ be a solution of ordinary differential equation (1.1w) generated by absolutely continuous functions The paper generalizing the Strook and Varadhan result [15] shows that the topological support of distributions of the process $(x(t))_{t\ge 0}$ coincides with the closure of the solutions set $\{X^\omega:\omega \text{ are absolutely continuous functions }\}$.