Hello.


I am studying stochastic process.


here,


I don't know what is difference of


"the process is homogeneous"
and
"the process is stationary"


I feel confusing. It seems to similar to me.



What is the difference between a homogeneous stochastic process and a stationary one?
A process is (strictly) stationary if any sequence of n consecutive points has the same distribution as any other sequence of n consecutive points. There are weaker definitions, for example weak stationarity is based only on the first two moments.


A (discrete valued) process is homogeneous if the transition probability between two given state values at any two times depends only on the difference between those times. 


However, some references uses "homogeneous" rather loosely and confuse the two concepts.


