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.

翻译：我们提出了一种融合经典蒙特卡洛模拟器与Wasserstein生成对抗网络的框架，用于建模、估计和模拟一类具有一般非平稳性和多维随机到达率的广泛到达过程。经典蒙特卡洛模拟器擅长捕捉随机对象中可解释的"物理机制"，而基于神经网络的模拟器则擅长捕捉高维分布中难以解释的复杂依赖关系。我们提出了一种融合随机生成神经网络与经典蒙特卡洛泊松模拟器的双重随机模拟器，以充分利用两者的优势。这种融合对基于真实数据估计模拟器的理论可靠性和计算可行性提出了挑战——该估计通过最小化模拟输出分布与真实数据分布之间的Wasserstein距离来实现。在理论性质方面，我们在非参数光滑性假设下证明了估计模拟器的一致性和收敛速率。在计算效率与估计过程可行性方面，我们解决了因蒙特卡洛泊松模拟器中不连续性导致的梯度评估难题。通过合成数据集与真实数据集的数值实验，验证了所提框架的性能。