Martingale markov chain

1. What is the difference between a martingale and a Markov chain?
2. Is a martingale always Markov?
3. What is martingale in stochastic process?
4. Can a Markov process of order one also be a martingale?

What is the difference between a martingale and a Markov chain?

Que : What is the difference between Markov Property and a Martingale? 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.

Is a martingale always Markov?

Martingale is a special case of Markov wth f = x and g = x. However for the process to be Markov we require for every function f a corresponding function g such that (6) holds. So not all Martingales are Markov.

What is martingale in stochastic process?

In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values.

Can a Markov process of order one also be a martingale?

A first-order Markov chain can be a martingale, but need not be. In order for it to be a martingale, you need E[Xn+1|Xn]=Xn.