Yes, in fact, this is a good example of processes that have the Markov property but DO NOT have independent increments. A process with independent increments satisfies the Markov property. However, not the other way round. Consider a IID sequence Zn = 1 or -1 on the toss of a coin (50/50) It's trivially Markov because P[Z2=1|Z1] = P[Z2=1|F1] (each coin toss is independent of the last, so knowing the history won't change our predictions of the future) Now, what is P[Z2 - Z1] = 2? 0.25, since we must have Z1 = -1 and Z2 = 1 But what if we know that Z1 - Z0 = 2. Now, what is P[Z2 - Z1] = 2? 0 - it's impossible because we must have Z0 = -1 and Z1 = 1. So, the increment Z1 - Z0 is NOT independent of Z2 - Z1 I'd arm myself with this example just in case they ask for one in the CT4 exam (though they never do!) Good luck! John
