We consider the Ornstein-Uhlenbeck (OU) process, a stochastic process widely used in finance, physics, and biology. Parameter estimation of the OU process is a challenging problem. Thus, we review traditional tracking methods and compare them with novel applications of deep learning to estimate the parameters of the OU process. We use a multi-layer perceptron to estimate the parameters of the OU process and compare its performance with traditional parameter estimation methods, such as the Kalman filter and maximum likelihood estimation. We find that the multi-layer perceptron can accurately estimate the parameters of the OU process given a large dataset of observed trajectories; however, traditional parameter estimation methods may be more suitable for smaller datasets.

翻译：我们考虑奥恩斯坦-乌伦贝克（OU）过程，这是一种广泛应用于金融、物理和生物学的随机过程。OU过程的参数估计是一个具有挑战性的问题。因此，我们回顾了传统跟踪方法，并将其与利用深度学习估计OU过程参数的新颖应用进行比较。我们使用多层感知器来估计OU过程的参数，并将其性能与卡尔曼滤波器和最大似然估计等传统参数估计方法进行比较。研究发现，在给定大量观测轨迹数据集的情况下，多层感知器能够准确估计OU过程的参数；然而，对于较小的数据集，传统参数估计方法可能更为适用。