If we have an integer valued stochastic process, are these implications correct?
independent increments $\rightarrow$ Markov property
Markov property $\nrightarrow$ independent increments
stationary increments $\rightarrow$ time homogenity
time homogenity $\nrightarrow$ stationary increments
stationary increments $\rightarrow$ independent increments $\rightarrow$ Markov Property
independent increments $\nrightarrow$ stationary increments
PS: I got number 2 answered by an example in another thread, but I would like to know all on this list aswell, because it is confusing for me. You don't need to make me examples if this is too much work for you, please then just tell me if the impliations hold or not.
I made a picture to describe it, is it correct?