stationary distribution

A stationary distribution, in probability theory, refers to a probability distribution for a Markov process that remains unchanged over time. This means that if a system is in a state described by the stationary distribution, it will continue to be in that distribution in the future.12

Markov processes are a type of stochastic process where the future state depends only on the current state, not on the past sequence of events that led to it. This "memoryless" property is fundamental to understanding how these processes evolve.34

When a Markov process with stationary transition probabilities runs for a long time, its distribution often converges to a stationary distribution, regardless of its initial state. This concept is crucial in various fields, including economics and statistical mechanics, where it describes systems that have reached a stable or unchanging condition.156