Stochastic process measurability conditions
Annales de l'Institut Fourier, Tome 25 (1975) no. 3-4, pp. 163-176.

Dans la définition de la séparabilité d’un processus stochastique, on remplace l’ensemble de séparabilité par un ensemble de temps optionnels (prévisibles). On obtient alors une propriété nouvelle, la séparabilité optionnelle (prévisible). Tout processus bien-mesurable (accessible) est séparable. Les démonstrations des propriétés de limites des processus séparables usuels deviennent alors les démonstrations des mêmes propriétés pour les processus bien-mesurables (prévisibles).

If the separability of the separable process definition is replaced by a set of optional (predictable) times, a new property is obtained, optional (predictable) separability. A well measurable (accessible) process is necessarily optionally (predictably) separable. Proofs of limit properties of a separable process become proofs of the same limit properties of a well measurable (predictable) process.

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     title = {Stochastic process measurability conditions},
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Doob, J. L. Stochastic process measurability conditions. Annales de l'Institut Fourier, Tome 25 (1975) no. 3-4, pp. 163-176. doi : 10.5802/aif.577. https://www.numdam.org/articles/10.5802/aif.577/

[1] D. G. Austin, G. A. Edgar and A. Ionescu Tulcea, Pointwise convergence in terms of expectations, to appear. | Zbl

[2] Kai Lai Chung, On the fundamental hypotheses of Hunt processes, Ist. Naz. Alta Mat., IX (1972), 43-52. | MR | Zbl

[3] Cl. Dellacherie, Capacités et processus stochastiques, Ergeb. Math. Grenzgebiete, 67 (1972). | MR | Zbl

[4] J.-F. Mertens, Théorie des processus stochastiques généraux. Applications aux surmartingales, Z. Wahrscheinlichkeitstheorie, 22 (1972), 45-68. | MR | Zbl

[5] P. A. Meyer, Le retournement du temps, d'après Chung et Walsh, Lecture Notes in Mathematics 191, Springer 1971, 213-236. | Numdam

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