Homogeneous Markov

Homogeneous Markov models, which assume constant transition probabilities over time, are being extended and refined to address the complexities of real-world systems where these probabilities often vary. Current research focuses on developing time-inhomogeneous models, incorporating techniques like modified Baum-Welch algorithms and multi-marginal optimal transport, to better capture dynamic processes and handle sparse or aggregated data. These advancements are improving the accuracy of predictions in diverse applications, from resource availability in smart cities to population flow estimation and algorithmic fairness in dynamical systems. The resulting models offer more realistic representations of complex systems and enable more effective decision-making in various fields.