Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
On liftings and the regularization of stochastic processes
Download PDF
Download PDF
  • Published: March 1988

On liftings and the regularization of stochastic processes

  • M. Talagrand1 nAff2 

Probability Theory and Related Fields volume 78, pages 127–134 (1988)Cite this article

  • 71 Accesses

  • 6 Citations

  • Metrics details

Summary

We show that not all liftings are suitable tools for the regularization of stochastic processes. Under Continuum hypothesis, we construct a Glivenko-Cantelli class Z on [0, 1] and a lifting ρ ofL ∞ such that ρZ is not a Glivenko-Cantelli class. This strongly contrasts with the fact, shown earlier by the author, that some special liftings have exellent regularization properties.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Fremlin, D.H.: Product of radon measures: a counter-example. Canad. Math. Bull.19, 285–289 (1976)

    Google Scholar 

  2. Ionescu-Tulcea, A., Ionescu-Tulcea, C.: Topics in the theory of lifting. Berlin Heidelberg New York: Springer 1969

    Google Scholar 

  3. Talagrand, M.: Closed convex hull of sets of measurable functions, Riemann-measurable functions and measurability of translations. Ann. Inst. FourierXXXII, 39–69 (1982)

    Google Scholar 

  4. Talagrand, M.: Pettis integral and measure theory. Mem. Amer. Math. Soc. vol. 307 (1984)

  5. Talagrand, M.: The Glivenko-Cantelli problem. Ann. Probab.15, 837–840 (1987)

    Google Scholar 

  6. Talagrand, M.: Measurability problems for empirical processes. Ann. Probab.15, 204–212 (1987)

    Google Scholar 

Download references

Author information

Author notes
  1. M. Talagrand

    Present address: Department of Mathematics, Ohio State University, 43210, Columbus, OH, USA

Authors and Affiliations

  1. Equipe d'analyse 4, Université de Paris VI, Place Jussieu, F-75230, Paris, France

    M. Talagrand

Authors
  1. M. Talagrand
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Talagrand, M. On liftings and the regularization of stochastic processes. Probab. Th. Rel. Fields 78, 127–134 (1988). https://doi.org/10.1007/BF00718040

Download citation

  • Revised: 16 November 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF00718040

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Suitable Tool
  • Regularization Property
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature