Kazamaki's condition

Template:One source 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 $({ℱ}_t{)}_{t\ge 0}$. If $(\exp (M_t/2){)}_{t\ge 0}$ is a uniformly integrable submartingale, then the Doléans-Dade exponential Ɛ(M) of M is a uniformly integrable martingale.

References

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