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Is it true that if a counting process has stationary increments, then it is time homogeneous?

stationary increments → time homogeneous?

And is it also true that independent increments gives Markovian property?

that is :

independent increments → markovian property ?

The opposite implications are false?

And is there a connection between stationary increments and the markovian property? I know that the nonhomogeneous poisson process is a markov process. So we can not say that markov → stationary increments, but can the opposite implication hold?

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# Stochastic processess

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