Poisson Process

Poisson processes, which model the occurrence of events at random points in time, are a fundamental tool in various scientific fields. Current research focuses on extending their applicability beyond homogeneous scenarios, incorporating hierarchical structures and non-homogeneous intensities to better represent real-world phenomena like financial trading volumes and space debris conjunctions. These advancements leverage techniques such as Bayesian methods, neural networks, and Markov Chain Monte Carlo simulations to improve model accuracy and efficiency, leading to more robust predictions and optimized decision-making in diverse applications. The resulting models find use in areas ranging from financial modeling and network optimization to space traffic management and generative modeling.