Killed Brownian transition density
= Killed Brownian transition density
{title2=$p_D(t,z,w)$}
The area density of $\mathbb P_z(B_t\in dw,\ t<T_D)$ for <planar Brownian motion> killed on its first exit from $D$. Its total mass is the survival probability, not generally one. Integrating this density over time gives the <Green function of killed planar Brownian motion>.