Consider an one-dimensional diffusion, with values in $(0,\infty)$, solution of the SDE
$$dX_t = \mu(m-X_t)dt + \sigma X^{\psi}_tdB_t$$
Where $B_t$ is a standard one-dimensional brownian motion, $m>0,\sigma>0,\mu>0,\psi \in (0,\frac{1}{2})$ and $X_0 \in (0,\infty)$.
Show that
a) This diffusion is positive recurrent
b) The stationary measure $\pi$ integrates $x^q$ for $q \in \mathbb{R}$
For the positive recurrence, one usually looks at the scale function. The thing is that the presence of the term $X^\psi_t$ on the diffusion function confuses me when building the scale function. Any help or insights are greatly appreciated.