I was wondering for a Markov process:
Is it true that:
it is a stationary process, iff its transition probability function is invariant to time-translation (i.e. it is homogeneous) and its initial distribution is invariant to time-translation?
- When the state space is discrete, is the limit of its transition probability function related to stationarity for the process? Is its stationary distribution related to stationarity, besides both have "stationary" in their names?
Thanks and regards!