Kazamaki's condition - Alchetron, The Free Social Encyclopedia

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 ≥ 0 be a continuous local martingale with respect to a right-continuous filtration ( F t ) t ≥ 0 . If ( exp ⁡ ( M t / 2 ) ) t ≥ 0 is a uniformly integrable submartingale, then the Doléans-Dade exponential Ɛ(M) of M is a uniformly integrable martingale.

References

Kazamaki's condition Wikipedia

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