Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Liftings and the construction of stochastic processes


Author: Donald L. Cohn
Journal: Trans. Amer. Math. Soc. 246 (1978), 429-438
MSC: Primary 60G05; Secondary 46G15
MathSciNet review: 515549
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if the continuum hypothesis holds, then the use of liftings to construct modifications of stochastic processes can replace measurable processes with nonmeasurable ones. The use of liftings to choose the paths, rather than the random variables, of a stochastic process is investigated.


References [Enhancements On Off] (What's this?)

  • [1] Donald L. Cohn, Measurable choice of limit points and the existence of separable and measurable processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 22 (1972), 161–165. MR 0305444 (46 #4574)
  • [2] R. M. Dudley, A counterexample on measurable processes, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 57–66. MR 0415747 (54 #3827a)
  • [3] J. Hoffmann-Jørgensen, Existence of measurable modifications of stochastic processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 25 (1972/73), 205–207. MR 0326818 (48 #5160)
  • [4] A. Ionescu Tulcea and C. Ionescu Tulcea, On the existence of a lifting commuting with the left translations of an arbitrary locally compact group, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) Univ. California Press, Berkeley, Calif., 1967, pp. 63–97. MR 0212122 (35 #2997)
  • [5] A. Ionescu Tulcea and C. Ionescu Tulcea, Liftings for abstract valued functions and separable stochastic processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 114–118. MR 0277026 (43 #2763)
  • [6] A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48, Springer-Verlag New York Inc., New York, 1969. MR 0276438 (43 #2185)
  • [7] Kiyosi Itô, The canonical modification of stochastic processes, J. Math. Soc. Japan 20 (1968), 130–150. MR 0226719 (37 #2306)
  • [8] Kiyoshi Itô, Canonical measurable random functions, Proc. Internat. Conf. on Functional Analysis and Related Topics (Tokyo, 1969), Univ. of Tokyo Press, Tokyo, 1970, pp. 369–377. MR 0281250 (43 #6969)
  • [9] Gabriel Mokobodzki, Relèvement borélien compatible avec une classe d’ensembles négligeables. Application à la désintégration des mesures, Séminaire de Probabilités, IX (Seconde Partie, Univ. Strasbourg, Strasbourg, années universitaires 1973/1974 et 1974/1975), Springer, Berlin, 1975, pp. 437–442. Lecture Notes in Math., Vol. 465. MR 0430781 (55 #3786)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60G05, 46G15

Retrieve articles in all journals with MSC: 60G05, 46G15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0515549-3
PII: S 0002-9947(1978)0515549-3
Article copyright: © Copyright 1978 American Mathematical Society