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XV: 45, 643-668, LNM 850 (1981)

**AUERHAN, J.**; **LÉPINGLE, Dominique**

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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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

Nature: Original

Retrieve article from Numdam