stationary transition probability

Stationary transition probabilities are a characteristic of Markovian processes where the probability of moving from one state to another remains constant over time. A Markov process is a type of stochastic process where the future state depends only on the current state, not on the sequence of events that preceded it.1

If a Markov process has stationary transition probabilities, its behavior over time can be predictable. As time progresses, the process often converges to a "stationary distribution," meaning it spends a certain proportion of time in different states, regardless of its starting point. This concept is fundamental in understanding various random phenomena, from simple random walks to more complex systems like Brownian motion.1