Que : What is the difference between Markov Property and a Martingale? Explanation by Sir John Potter:- Markov and Martingale are not really connected... Markov means where go next depends at most on where we are now. Any process with independent increments has the Markov property, eg Brownian motion. Martingale means that we expect the future value to be the current value. Standard Brownian motion has the Markov property and is a martingale. General Brownian motion with drift has the Markov property and is NOT a martingale. Let Xn = Xn-1 + Zn X0, where Zn ~ N(a,1) This is NOT Markov because where we go next, Xn, depends not just on where we are now, Xn-1, but also on where we were in the past, X0. If a=0, Xn is a martingale If a <>0, Xn is not a martingale. So, we have created a 2*2 grid here of Markov/NOT Markov versusMartingale/NOT Martingale.
