Hello 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?