论文标题
路径依赖性McKean-Vlasov随机微分方程的参数估计
Parameter estimation of path-dependent McKean-Vlasov stochastic differential equations
论文作者
论文摘要
这项工作涉及一类依赖路径依赖的McKean-Vlasov随机微分方程，具有未知参数。首先，我们证明了这些方程在非lipschitz条件下的存在和唯一性。其次，我们构建这些参数的最大似然估计器，然后讨论它们的强一致性。第三，提供了一种数值模拟方法，用于提供路径依赖性的麦凯恩 - 维拉索夫随机微分方程。此外，我们估计了这些方程式解决方案与其数值方程的误差。最后，我们举例说明我们的结果。
The work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters. First, we prove the existence and uniqueness of these equations under non-Lipschitz conditions. Second, we construct maximum likelihood estimators of these parameters and then discuss their strong consistency. Third, a numerical simulation method for the class of path-dependent McKean-Vlasov stochastic differential equations is offered. Moreover, we estimate the errors between solutions of these equations and that of their numerical equations. Finally, we give an example to explain our result.
