If a question asks for the proportion of time spent in a specific state is this the same as the stationary distribution or something else? For continuous time Markov chain with finite state space.
2026-03-27 21:37:33.1774647453
Continuous time Markov chain. proportion of time spent in state i
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Yes, that'll be the steady state distribution of the state. This happens because of the regenerative structure of the CTMC and thus long time fraction of time spent in a state becomes equal to its steady state probability. So, it is not special for CTMC's but is true for all kind of regenerative processes.