VIII: 05, 25-26, LNM 381 (1974)
DELLACHERIE, Claude
Intégrales stochastiques par rapport aux processus de Wiener et de Poisson (General theory of processes)
This paper shows that the previsible representation property of Brownian motion and the (compensated) Poisson processes is a consequence of the Wiener and Poisson measures being unique solutions of martingale problems
Comment: A gap in the proof is filled in 928 and 2002. This is a very important paper, opening the way to a series of investigations on the relations between previsible representation and extremality. See Jacod-Yor, Z. für W-theorie, 38, 1977 and Yor 1221. For another approach to the restricted case considered here, see Ruiz de Chavez 1821. The previsible representation property of Brownian motion and compensated Poisson process was know by Itô; it is a consequence of the (stronger) chaotic representation property, established by Wiener in 1938. The converse was also known by Itô: among the martingales which are also Lévy processes, only Brownian motions and compensated Poisson processes have the previsible representation property
Keywords: Brownian motion, Poisson processes, Previsible representation
Nature: Original
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