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XII: 21, 265-309, LNM 649 (1978)

**YOR, Marc**; **SAM LAZARO, JosÃ© de**

Sous-espaces denses dans $L^1$ ou $H^1$ et reprÃ©sentation des martingales (Martingale theory)

This paper was a considerable step in the study of the general martingale problem, i.e., of the set ${\cal P}$ of all laws on a filtered measurable space under which a given set ${\cal N}$ of (adapted, right continuous) processes are local martingales. The starting point is a theorem from measure theory due to R.G. Douglas (*Michigan Math. J.* 11, 1964), and the main technical difference with preceding papers is the systematic use of stochastic integration in $H^1$. The main result can be stated as follows: given a law $P\in{\cal P}$, the set ${\cal N}$ has the previsible representation property, i.e., ${\cal F}_0$ is trivial and stochastic integrals with respect to elements of ${\cal N}$ are dense in $H^1$, if and only if $P$ is an extreme point of ${\cal P}$. Many examples and applications are given

Comment: The second named author's contribution concerns only the appendix on homogeneous martingales

Keywords: Previsible representation, Douglas theorem, Extremal laws

Nature: Original

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Sous-espaces denses dans $L^1$ ou $H^1$ et reprÃ©sentation des martingales (Martingale theory)

This paper was a considerable step in the study of the general martingale problem, i.e., of the set ${\cal P}$ of all laws on a filtered measurable space under which a given set ${\cal N}$ of (adapted, right continuous) processes are local martingales. The starting point is a theorem from measure theory due to R.G. Douglas (

Comment: The second named author's contribution concerns only the appendix on homogeneous martingales

Keywords: Previsible representation, Douglas theorem, Extremal laws

Nature: Original

Retrieve article from Numdam