Stationary Distribution

A stationary distribution describes the long-term behavior of a system, representing the probability of finding the system in a particular state after it has reached equilibrium. Current research focuses on characterizing and efficiently computing stationary distributions for various systems, including those modeled by stochastic differential equations, Markov decision processes, and queueing systems, often employing machine learning techniques like neural networks and generative adversarial networks. Understanding stationary distributions is crucial for diverse applications, from optimizing machine learning algorithms and analyzing financial time series to improving the efficiency of queueing systems and developing robust anomaly detection methods.