Parameter Estimation for Rough Differential Equations with Applications to Multiscale Modelling

本提案寻求对PDRA（一年）的支持，Christophe Ladroue博士。第一个目标是开发和实现由粗糙路径驱动的微分方程的统计估计和推理方法。这种微分方程是非常普遍的，可以用来模拟大量的动力系统。我们的动机来自于多尺度建模，因为我们希望我们将开发的方法可以用于重要的应用，如分子动力学或气候建模。第二个目标是用小尺度随机微分方程近似多尺度随机微分方程（SDE）的慢过程。最后的目标是使用我们的参数估计方法来获得一些关于使用多尺度系统的短路径的慢过程的极限动力学的信息。

This proposal seeks support for a PDRA (one year), Dr. Christophe Ladroue. The first goal is to develop and implement methods for statistical estimation and inference in the context of differential equations driven by rough paths (RDEs). Such differential equations are very general and can be used to model a large number of dynamical systems. Our motivation comes from multiscale modelling as we hope the approach we will develop could be useful for important applications, such as molecular dynamics or climate modelling. The second goal is to approximate the slow process of a multiscale stochastic differential equation (SDE) by an RDE at small scales. The final goal would be to use our parameter estimation methods to get some information about the limiting dynamics of the slow process using short paths of the multiscale system.