Stochastic process measurability conditions

J. L. Doob

Annales de l'institut Fourier (1975)

  • Volume: 25, Issue: 3-4, page 163-176
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Doob, J. L.. "Stochastic process measurability conditions." Annales de l'institut Fourier 25.3-4 (1975): 163-176. <http://eudml.org/doc/74239>.

@article{Doob1975,
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.},
author = {Doob, J. L.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3-4},
pages = {163-176},
publisher = {Association des Annales de l'Institut Fourier},
title = {Stochastic process measurability conditions},
url = {http://eudml.org/doc/74239},
volume = {25},
year = {1975},
}

TY - JOUR
AU - Doob, J. L.
TI - Stochastic process measurability conditions
JO - Annales de l'institut Fourier
PY - 1975
PB - Association des Annales de l'Institut Fourier
VL - 25
IS - 3-4
SP - 163
EP - 176
AB - 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.
LA - eng
UR - http://eudml.org/doc/74239
ER -

References

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  1. [1] D. G. AUSTIN, G. A. EDGAR and A. Ionescu TULCEA, Pointwise convergence in terms of expectations, to appear. Zbl0276.60034
  2. [2] Kai Lai CHUNG, On the fundamental hypotheses of Hunt processes, Ist. Naz. Alta Mat., IX (1972), 43-52. Zbl0242.60031MR50 #11474
  3. [3] Cl. DELLACHERIE, Capacités et processus stochastiques, Ergeb. Math. Grenzgebiete, 67 (1972). Zbl0246.60032MR56 #6810
  4. [4] J.-F. MERTENS, Théorie des processus stochastiques généraux. Applications aux surmartingales, Z. Wahrscheinlichkeitstheorie, 22 (1972), 45-68. Zbl0236.60033MR49 #11616
  5. [5] P. A. MEYER, Le retournement du temps, d'après Chung et Walsh, Lecture Notes in Mathematics 191, Springer 1971, 213-236. 

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