Given that $N_{t}$ is a Poisson random measure with $\mathbb{E}[N]=\lambda t$, then
$N_{t}-\lambda t$ is a martingale.
Okay, now I don't get why in every Poisson random measure they always get the compensated random measure. What's the point of compensating a random process? I ask this because I'm studying Ito's lemma applied to jump processes.
Thanks in advance.