Before revision:  In a recent paper, for particular stochastic Petri net models, we proposed a jump diffusion approximation that extends Kurtz's diffusion approximation to the case when the process reaches the boundary with non-negligible probability.
After revision:  In a recent paper, for particular stochastic Petri net models, we proposed a jump diffusion approximation that aims at being applicable beyond the limits of Kurtz's diffusion approximation to the case when the process reaches the boundary with non-negligible probability.