From lecture notes on SDE's.
Consider the Stratonovich equation $dX_t=rX_tdt+\sigma X_t\circ dB_t$. It has initial condition $X_0=x$. What are the conditions for the parameters $(\sigma,r)$, for $\mathbb{E}(X_t)$ and $\mathbb{E}(X_t^2)$ to stay bounded as $t\rightarrow \infty$?
I thought about using the Dynkin formula, but I think this has more to do with stochastic stability? I am not sure which theorem to use, at there does not seem to be some general approach?