It seems to me that Stationary increment => Homo Markov.  But I don't
quite believe it.  Can anyone tell me if/why I am wrong?

My reasoning is:

Stationary increment => X(t+h)-X(s+h) has same dist.with X(t)-X(s)
So, given the current state X(S), then X(t) is decided statistically.
It seems X(t) does not need states before X(s) anymore.  Anything wrong?

I believe Homo Markov=> Stationary increment, though.  [tell me if I am wrong]

Thanks!

Frank
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