I would like to ask if there is a way to find the expected value and the variance of the following process $$ dv_t=(a-be^{\alpha v_t})dt+\sigma dW_t, \quad v_t=v_0 $$ where $a\in (-\infty,+\infty), b>0, \sigma>0, \alpha>0$.

Thank you for your time. I truly appreciate it.

**Added** (after the question of The Bridge)

Let $V_t=e^{2v_t}$, then applying Ito's lemma we can show that

$$ V_t=\frac{V_0\exp(2at +2\sigma W_t)}{\left(1+\alpha b V_0^{\alpha/2}\int_0^t exp(\alpha(as+\sigma W_s))ds\right)^{\alpha/2}} $$ From here, we can see that the above SDE has a unique solution.