A General Framework to Simulate Diffusions with Discontinuous Coefficients and Local Times
提出一种基于连续时间马尔可夫链近似的通用模拟方法，用于求解具有不连续系数和局部时间项的随机微分方程，在状态空间离散化方面优于传统时间离散化方案，并通过数值算例验证了精度和稳健性。
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.