In this article, we propose an efficient general simulation method for diffusions that are solutions to stochastic differential equations with discontinuous coefficients and local time terms. The proposed method is based on sampling from the corresponding continuous-time Markov chain approximation. In contrast to existing time discretization schemes, the Markov chain approximation method corresponds to a spatial discretization scheme and is demonstrated to be particularly suited for simulating diffusion processes with discontinuities in their state space. We establish the theoretical convergence order and also demonstrate the accuracy and robustness of the method in numerical examples by comparing it to the known benchmarks in terms of root mean squared error, runtime, and the parameter sensitivity.

在本文中，我们提出了一种有效的一般扩散模拟方法，该方法是具有不连续系数和本地时间项的随机微分方程的解。所提出的方法基于从相应的连续时间马尔可夫链近似中采样。与现有的时间离散化方案相比，马尔可夫链近似方法对应于空间离散化方案，并且被证明特别适用于模拟在其状态空间中具有不连续性的扩散过程。我们建立了理论收敛顺序，并通过在均方根误差、运行时间和参数敏感性方面将其与已知基准进行比较，在数值示例中证明了该方法的准确性和鲁棒性。