Centered square-integrable Lévy martingale
= Centered square-integrable Lévy martingale
If a Lévy process has mean zero and $\operatorname{Var}(X_1)=\sigma^2<\infty$, then $\operatorname{Var}(X_t)=t\sigma^2$ and $X_t^2-t\sigma^2$ is a martingale.
= Centered square-integrable Lévy martingale
If a Lévy process has mean zero and $\operatorname{Var}(X_1)=\sigma^2<\infty$, then $\operatorname{Var}(X_t)=t\sigma^2$ and $X_t^2-t\sigma^2$ is a martingale.