SUPPORT THEOREM FOR THE POSITIVE RANDOM EVOLUTION EQUATION IN H"{O}LDER NORM

Let's consider the stochastic differential equation \[\left\{ \begin{split} dX_t&=\sigma(X_t,V_t )dW_t+b(X_t,R_t)dt\\ X_0&=x>0 \end{split}\right. \] In this paper, we establish support theorem for positive random evolution type on $C^{\alpha,0}([0;1];\mathbb{R})$. We use linear interpolations of $W$ proof.