Stationary Probabilities
时间: 2024-01-21 17:04:35 浏览: 56
Stationary probabilities refer to the probabilities of a Markov chain reaching a particular state in the long run, after it has been running for a long time. In other words, stationary probabilities are the probabilities of a Markov chain being in a particular state, independent of its initial state, after it has run for a sufficiently long time.
To calculate the stationary probabilities of a Markov chain, we need to solve a set of linear equations known as the balance equations. The balance equations state that the rate at which the Markov chain leaves a particular state must be equal to the rate at which it enters that state. By solving these equations, we can find the stationary probabilities for each state in the Markov chain.
The stationary probabilities of a Markov chain are important because they provide insights into the long-term behavior of the system. For example, if a particular state has a high stationary probability, it means that the system is likely to spend a lot of time in that state. On the other hand, if a state has a low stationary probability, it means that the system is unlikely to spend much time in that state.