So I have $W_t$ is a Wiener process where $X_t = W_t^2-t$. I need to prove $X_t$ is a martingale.
I know that in order to prove $X-t$ is a Martingale, we must have:
1) $\mathbb E[|X_t|]<∞$
2) $\mathbb E[X_t|F_s]=X_s $ for $0 ≤ s ≤ t$
I have started applying these properties to my question but none of the examples I have are similar to this one. So far I have:
$\mathbb E[|X_t|] = \mathbb E[|W_t^2 -t|]$ = $\int_∞^∞ w -t dw$ and $\int_∞^∞ -(w -t) dw$
I am not sure if these are correct, can anyone point me in the right direction?