This question pertains to the topic titled: Is this local martingale a true martingale?
(Find it here!)
"Using the Ito's formula I have shown that $X_t$ is a local martingale, because $\mathrm{d}X_t = \underline{\phantom{b_t}} \mathrm{d} B_t$",
Can someone please explain this opening phrase to the original question to me further? I can not get my head around why $X_t$ would not indeed be a true martingale if it is written in this form (all Ito integrals are martingales! (?)).