# The same expectation means martingale?

If a stochastic process has the same expectation value for all pisitive t, then is it a martingale? I don’t know how to show it whether that is right.

The Brownian motion $$W_t$$ is a martingale because for all $$u>t$$: $$W_t = E(W_u | \mathcal{F}_t),$$
However, the process $$X_t$$
$$X_t = 1_{\{a has 0 expectation but is not a martingale.
• I just added the dot between 2 and 1, this process takes value +1 or -1 between a and b, but it is not a martingale as it goes back to 0 for $t>b$ – Sebapi Dec 10 '18 at 15:50