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In mathematics Kazamaki's condition gives a sufficient criterion ensuring that the Doléans-Dade exponential of a local martingale is a true martingale. This is particularly important if Girsanov's theorem is to be applied to perform a change of measure. Kazamaki's condition is more general than Novikov's condition.

Statement of Kazamaki's condition

Let $M=(M_t{)}_{t\ge 0}$ be a continuous local martingale with respect to a right-continuous filtration $({\mathcal{ℱ}}_t{)}_{t\ge 0}$. If $(\exp (M_t/2){)}_{t\ge 0}$ is a uniformly integrable submartingale, then the Doléans-Dade exponential PROPERTY builders did not have the simplest year, what with the cooling measures imposed in January and the loan curbs in June, but some still managed to do effectively while others made their first foray abroad.

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References

• Daniel Revuz, Marc Yor: Continuous Martingales and Brownian motion. Springer-Verlag, New York 1999, ISBN 3-540-64325-7.