  We propose a framework that integrates classical Monte Carlo simulators and
Wasserstein generative adversarial networks to model, estimate, and simulate a
broad class of arrival processes with general non-stationary and
multi-dimensional random arrival rates. Classical Monte Carlo simulators have
advantages at capturing the interpretable "physics" of a stochastic object,
whereas neural-network-based simulators have advantages at capturing
less-interpretable complicated dependence within a high-dimensional
distribution. We propose a doubly stochastic simulator that integrates a
stochastic generative neural network and a classical Monte Carlo Poisson
simulator, to utilize both advantages. Such integration brings challenges to
both theoretical reliability and computational tractability for the estimation
of the simulator given real data, where the estimation is done through
minimizing the Wasserstein distance between the distribution of the simulation
output and the distribution of real data. Regarding theoretical properties, we
prove consistency and convergence rate for the estimated simulator under a
non-parametric smoothness assumption. Regarding computational efficiency and
tractability for the estimation procedure, we address a challenge in gradient
evaluation that arise from the discontinuity in the Monte Carlo Poisson
simulator. Numerical experiments with synthetic and real data sets are
implemented to illustrate the performance of the proposed framework.
