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J. L. Doob
Stochastic process measurability conditions
Annales de l'institut Fourier, 25 no. 3-4 (1975), p. 163-176, doi: 10.5802/aif.577
Article PDF | Reviews MR 54 #8817 | Zbl 0287.60032

Résumé - Abstract

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.

Bibliography

[1] D. G. AUSTIN, G. A. EDGAR and A. Ionescu TULCEA, Pointwise convergence in terms of expectations, to appear.  Zbl 0276.60034
[2] Kai Lai CHUNG, On the fundamental hypotheses of Hunt processes, Ist. Naz. Alta Mat., IX (1972), 43-52.  MR 50 #11474 |  Zbl 0242.60031
[3] Cl. DELLACHERIE, Capacités et processus stochastiques, Ergeb. Math. Grenzgebiete, 67 (1972).  MR 56 #6810 |  Zbl 0246.60032
[4] J.-F. MERTENS, Théorie des processus stochastiques généraux. Applications aux surmartingales, Z. Wahrscheinlichkeitstheorie, 22 (1972), 45-68.  MR 49 #11616 |  Zbl 0236.60033
[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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