Derive Laplace Equation through Random Walk

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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!