= Void probability for growing Poisson rain patches
{title2=$\mathbb P(\xi\text{ dry at }\tau)=e^{-\mu(A_{\xi,\tau})}$}
For drops with intensity $\lambda(x,t,v)$, impact time $t$ and nonnegative <volume> $v$, let their radius at time $\tau$ be $r(\tau-t,v)$. The dry <probability> at $\xi$ is
$$
\exp\left[-\int_{t\le\tau}\int_{v\ge0}\int_{|x-\xi|\le r(\tau-t,v)}\lambda(x,t,v)\,dx\,dv\,dt\right].
$$
The exponent is the intensity of drops whose patch covers the point by that time. An infinite exponent means zero dry <probability>. No spatial-homogeneity assumption is needed.
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