Here is an interesting article from Wikipedia: First-hitting-time model
I am particularly interested in how the following density is derived:
$$p\left(x,t;x_0,x_c\right)=\frac{1}{\sqrt{4 \pi D t}}\left( e^{-\frac{\left(x-x_c\right){}^2}{4 D t}}-e^{-\frac{\left(x-\left(2 x_c-x_0\right)\right){}^2}{4 D t}}\right)$$
Can anyone provide some hints?