# Are invariant and stationary distribution the same thing?

I am reading a material about Markov chains and in it the author works on the Markov chains part discrete the invariant distribution of the process. However, when addressing the part of continuous Markov chains he stops to consider the stationary distribution and no longer mentions the term invariant distribution. I wonder if they are the same thing? Or did I get lost in something?

• Invariance is a more general property. Invariance may hold through space, not only through time... A stationary Markov chain is usually called homogeneous Markov chain... In general, do not get fixated on the terminology preferences of one person. When in doubt, check against terminology on the web. – stans Jan 23 at 2:49