Limit theorems for number of diffusion processes which did not absorb by boundaries

We have random number of independent diffusion processes with absorption on boundaries in some region at initial time $t=0$. The initial numbers and positions of processes in region is defined by Poisson random measure. It is required to estimate of number of the unabsorbed processes for the fixed time \~$\tau>0$. The Poisson random measure depends on $\tau$ and $\tau\to\infty$.