Abstract
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 the support theorem for this positive random evolution equation type on $C^{\alpha,0}([0;1];\mathbb{R})$. We use the linear interpolations of $W$ for the proof.
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