Given $Z(t) = [w(t)]^2 -t $. I need to show that this is a martingale.
I need to show that $\mathbb{E}(z_t|f(s)]=z(s)$.
I start by:
$\mathbb{E}(z_t|f(s)] = \mathbb{E}[(w(t))^2 - (w(s))^2 + (w(s))^2 -t |f(s)]$
$= \mathbb{E}[(w(t))^2-(w(s))^2|f(s)].[(w(s)^2-t] $
Then I am stuck. I don't know how to go further.