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XI: 02, 21-26, LNM 581 (1977)

**BENVENISTE, Albert**

Application d'un théorème de G. Mokobodzki à la théorie des flots (Ergodic theory, General theory of processes)

The purpose of this paper is to extend to the theory of filtered flows (for which see 901 and 902) the dual version of the general theory of processes due to Azéma (for which see 814 and 937), in particular the association with any measurable process of suitable projections which are homogeneous processes. An important difference here is the fact that the time set is the whole line. Here the class of measurable processes which can be projected is reduced to a (not very explicit) class, and a commutation theorem similar to Azéma's is proved. The proof uses the technique of*medial limits * due to Mokobodzki (see 719), which in fact was developed precisely at the author's request to solve this problem

Keywords: Filtered flows, Stationary processes, Projection theorems, Medial limits

Nature: Original

Retrieve article from Numdam

XIV: 46, 475-488, LNM 784 (1980)

**WEBER, Michel**

Sur un théorème de Maruyama (Gaussian processes, Ergodic theory)

Given a stationary centered Gaussian process $X$ with spectral measure $\mu$, a new proof is given of the fact that if $\mu$ is continuous, the flow of $X$ is weakly mixing

Keywords: Stationary processes

Nature: Original

Retrieve article from Numdam

Application d'un théorème de G. Mokobodzki à la théorie des flots (Ergodic theory, General theory of processes)

The purpose of this paper is to extend to the theory of filtered flows (for which see 901 and 902) the dual version of the general theory of processes due to Azéma (for which see 814 and 937), in particular the association with any measurable process of suitable projections which are homogeneous processes. An important difference here is the fact that the time set is the whole line. Here the class of measurable processes which can be projected is reduced to a (not very explicit) class, and a commutation theorem similar to Azéma's is proved. The proof uses the technique of

Keywords: Filtered flows, Stationary processes, Projection theorems, Medial limits

Nature: Original

Retrieve article from Numdam

XIV: 46, 475-488, LNM 784 (1980)

Sur un théorème de Maruyama (Gaussian processes, Ergodic theory)

Given a stationary centered Gaussian process $X$ with spectral measure $\mu$, a new proof is given of the fact that if $\mu$ is continuous, the flow of $X$ is weakly mixing

Keywords: Stationary processes

Nature: Original

Retrieve article from Numdam