The following exercise is from a course on SDE's and I am a bit stumped. Consider the process.
$dX_t=\lambda\left(\xi-X_t \right)dt+\gamma\sqrt{|X_t|}dB_t$
$\lambda,\xi,\gamma>0$
Find $\mathbb{P}^{X_t=x}\left( X_t>2\right)$.
Now I would start by finding transition probabilities $p(t\rightarrow T,x\rightarrow X_T)$ in the backwards kolmogorov equation $\frac{\partial p}{\partial t }+Lp=0$, where $L$ is the generator for the diffusion. How would I then find the relevant area in the state space? And how to find the solution to the kolmogorov equation for these parameters?