The paper presents a comparison of traditional and deep learning methods for parameter estimation of the Ornstein-Uhlenbeck (OU) process, a stochastic process widely used in finance, physics, and biology.
The authors first review the discretization of the OU process and traditional parameter estimation methods, such as least squares estimation (LSE) and the Kalman filter. They then introduce the use of a multi-layer perceptron (MLP) as a stochastic parameter estimator for the OU process.
The authors conduct experiments to compare the performance of the MLP with traditional parameter estimation methods. They generate a dataset of observed trajectories of the OU process and train the MLP on this dataset. The results show that the MLP can accurately estimate the parameters of the OU process given a large dataset, but traditional methods like the Kalman filter and maximum likelihood estimation may be more suitable for smaller datasets.
The authors also discuss the universal approximation theorem, which suggests that a feedforward neural network with a single hidden layer can approximate any continuous function on a compact subset of Rn to arbitrary accuracy. This provides a theoretical basis for the MLP's ability to learn the parameters of the OU process.
Finally, the authors propose several directions for future work, including investigating the performance of the MLP with different architectures and hyperparameters, exploring the use of other deep learning models, and testing the performance with different datasets and types of noise.
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