1. ## Prove martingale

Hi all, I have been asked to prove the following process is martingale:
exp{aX(t) - 1/2 * a^2t} where X(t) is a standard Brownian motion. I'm stuck with this question and would really appreciate it if anyone could give me any suggestions on how to do it. Thanks very much in advance!

2. i would start by writing the process as a stochastic differential equation using ito's lemma. if the process is indeed a martingale, the drift term (dt) in ito should fall out. you will be left with your diffusion term. from here, you only need prove that the SDE is integrable.