论文标题
用于路径依赖性麦基·弗拉索夫方程的数值模拟的粒子方法
Particle method for the numerical simulation of the path-dependent McKean-Vlasov equation
论文作者
论文摘要
我们提出了粒子方法，用于模拟依赖路径依赖性的麦凯恩 - vlasov方程，其中漂移和扩散系数都取决于过程的整个轨迹，直到当前时间t，以及相应的边缘分布。我们的论文为这种数值方法建立了明确的收敛速率。我们通过记忆的修改后的Ornstein-Uhlenbeck过程的数值模拟来说明我们的发现，并扩展了Jansen-rit均值场模型的神经质量。
We present the particle method for simulating the solution to the path-dependent McKean-Vlasov equation, in which both the drift and the diffusion coefficients depend on the whole trajectory of the process up to the current time t, as well as on the corresponding marginal distributions. Our paper establishes an explicit convergence rate for this numerical approach. We illustrate our findings with numerical simulations of a modified Ornstein-Uhlenbeck process with memory, and of an extension of the Jansen-Rit mean-field model for neural mass.
