On the Support of the Solutions of Stochastic Differential Equations

Let x = (x(t))t 0 be a solution of stochastic differential equation (1.1m) generated by a continuous semimartingale and let x^ω = (x^ω (t))t 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 0 coincides with the closure of the solutions set {X^ω :\,ω are absolutely continuous functions}.