Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Liftings and the construction of stochastic processes
HTML articles powered by AMS MathViewer

by Donald L. Cohn PDF
Trans. Amer. Math. Soc. 246 (1978), 429-438 Request permission

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
  • 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 305444, DOI 10.1007/BF00532735
  • 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
  • J. Hoffmann-Jørgensen, Existence of measurable modifications of stochastic processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 25 (1972/73), 205–207. MR 326818, DOI 10.1007/BF00535892
  • 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
  • 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 277026, DOI 10.1007/BF00537015
  • 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, DOI 10.1007/978-3-642-88507-5
  • Kiyosi Itô, The canonical modification of stochastic processes, J. Math. Soc. Japan 20 (1968), 130–150. MR 226719, DOI 10.2969/jmsj/02010130
  • Kiyoshi Itô, Canonical measurable random functions, Proc. Internat. Conf. on Functional Analysis and Related Topics (Tokyo, 1969) Univ. Tokyo Press, Tokyo, 1970, pp. 369–377. MR 0281250
  • 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), Lecture Notes in Math., Vol. 465, Springer, Berlin, 1975, pp. 437–442. MR 0430781
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
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 246 (1978), 429-438
  • MSC: Primary 60G05; Secondary 46G15
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0515549-3
  • MathSciNet review: 515549