 Void probability for growing Poisson rain patches

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 $\xi$ isThe 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.