Ornstein Uhlenbeck Process

The Ornstein-Uhlenbeck (OU) process, a stochastic model describing mean-reverting systems, is a focus of ongoing research due to its applicability across diverse fields, from finance and physics to generative modeling. Current research emphasizes parameter estimation using both traditional methods (e.g., Kalman filtering, maximum likelihood estimation) and deep learning approaches (e.g., multilayer perceptrons, transformers), with a particular interest in improving accuracy and efficiency. The OU process serves as a foundation for understanding and developing advanced models, such as diffusion-based generative models and methods for analyzing complex time series data, impacting fields ranging from image restoration to financial forecasting. Its mathematical tractability makes it a valuable tool for theoretical analysis and algorithm development in stochastic processes.