# Kazamaki's condition

Let ${\displaystyle M=(M_{t})_{t\geq 0}}$ be a continuous local martingale with respect to a right-continuous filtration ${\displaystyle ({\mathcal {F}}_{t})_{t\geq 0}}$. If ${\displaystyle (\exp(M_{t}/2))_{t\geq 0}}$ is a uniformly integrable submartingale, then the Doléans-Dade exponential Ɛ(M) of M is a uniformly integrable martingale.