Stationary Distribution

A stationary distribution describes a stable, long-term pattern in a stochastic system, such as a Markov chain. It represents the probabilities of being in each state after the system has run for a long time, regardless of where it started. Essentially, it’s the equilibrium distribution that the system settles into, where the likelihood of being in each state remains constant over time. This concept helps analyze the behavior of complex systems like web surfing, stock prices, or queueing processes by showing which states are most frequently occupied in the long run.