XV: 41, 604-617, LNM 850 (1981)
LÉPINGLE, Dominique;
MEYER, Paul-André;
YOR, Marc
Extrémalité et remplissage de tribus pour certaines martingales purement discontinues (
General theory of processes,
Martingale theory)
This paper consists roughly of two parts. First, the study of a filtration where all martingales are purely discontinuous, and jump on a given well-ordered optional set. Then under a simple separability assumption, one can construct one single martingale which generates the filtration. The second part deals with the same problem as in
1540, but replacing continuous martingales by purely discontinuous martingales with unit jumps, and Brownian motion by a Poisson process. It is shown that the situation is much simpler, purity and extremality being equivalent in this case
Keywords: Poisson processes,
Pure martingales,
Previsible representation,
JumpsNature: Original
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