Consider general homogeneous Markov process $\{X_n\}_{n\in T}$. It means that time can be continuous or discrete and also random variables $X_n$ can be continuous or discrete, for $n\in T$.
I would like to know, that if Markov process $\{X_n\}_{n\in T}$ has unique stationary distribution than it is also limit distribution for this Markov process.
Anny help will be appreciated. Thanks.