I am looking for the solution of this problem:
Consider a bounded domain $\Omega\subset\mathbb{R}^2$ and let $u(x,y)$ be the probability of exiting $\Omega$ starting at $p=(x,y)$, assuming that the particle at $p$
moves in direction $\pm h(\cos\alpha,\sin\alpha)$ with probability $\frac{q}{2}$,
moves in direction $\pm h(-\sin\alpha,\cos\alpha)$ with probability $\frac{1-q}{2}$,
where $\alpha=\alpha(p)$ and $q=q(p)$. Derive the pde for which $u$ is a solution.
The fact is that I don't understand how to proceed, is there any book where I could find a similar problem?
Thanks in advance!