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XIV: 22, 200-204, LNM 784 (1980)
AUERHAN, J.; LÉPINGLE, Dominique; YOR, Marc
Construction d'une martingale réelle continue de filtration naturelle donnée (General theory of processes)
It is proved in 1123 that, under a mere separability assumption, any filtration is the natural filtration of some bounded left-continuous increasing process $(A_t)$. If the filtration contains a Brownian motion $(B_t)$, then it is also the natural filtration of the continuous martingale $\int_0^t A_sdB_s$. Therefore, the natural filtration of (finitely or countably) many independent Brownian motions is generated by a single continuous martingale. Explicit constructions are discussed
Nature: Original
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XV: 45, 643-668, LNM 850 (1981)
Les filtrations de certaines martingales du mouvement brownien dans ${\bf R}^n$ (II) (General theory of processes, Brownian motion, Martingale theory)
This is a sequel to 1336. The problem is to describe the filtration of the continuous martingale $\int_0^t (AX_s,dX_s)$ where $X$ is a $n$-dimensional Brownian motion. It is shown that if the matrix $A$ is normal (rather than symmetric as in 1336) then this filtration is that of a (several dimensional) Brownian motion. If $A$ is not normal, only a lower bound on the multiplicity of this filtration can be given, and the problem is far from solved. The complex case is also considered. Several examples are given
Comment: Further results are given by Malric Ann. Inst. H. Poincaré 26 (1990)
Nature: Original
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