Doob-Meyer decomposition theorem

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The Doob-Meyer decomposition theorem is a theorem in stochastic calculus about how a submartingale may be decomposed in a unique way into a Martingale and a continuous increasing process. It is named for J. L. Doob and Paul-André Meyer.

[edit] The theorem

If X_t is a continuous submartingale such that the set

{X_τ}

(where is a stopping time) is uniformly integrable, then there exists a continuous martingale M_t and a continuous increasing process A_t such that

almost surely.

The processes M_t and A_t are unique to the point of indistinguishability.

[edit] External links

• The Doob-Meyer decomposition theorem with proof, by Jan van Neerven