Skip to main content

On Lévy’s Equivalence Theorem in Skorohod Space

  • Conference paper
  • First Online:
High Dimensional Probability VI

Part of the book series: Progress in Probability ((PRPR,volume 66))

  • 1388 Accesses

Abstract

A new and simple proof of Lévy’s Equivalence Theorem in Skorohod space is given. This result and its consequences complement and complete the recent work of the authors [1].

Mathematics Subject Classification (2010). 60G50; 60G07.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Basse-O’Connor and J. Rosiński, On the uniform convergence of random series in Skorohod space and representations of càdlàg infinitely divisible processes. Ann. Probab. (2012). (To appear.)

    Google Scholar 

  2. P. Billingsley, Convergence of Probability Measures. 2nd Edition, Probability and Statistics. New York:Joh n Wiley & Sons, Inc., 1999.

    Google Scholar 

  3. P.Z. Daffer and R.L. Taylor, Laws of large numbers for [0, 1]. Ann. Probab. 7 (1979), 85–95.

    Article  MathSciNet  MATH  Google Scholar 

  4. S.N. Ethier and T.G. Kurtz, Markov Processes. Characterization and Convergence. Probability and Mathematical Statistics. New York:Joh n Wiley & Sons Inc., 1986.

    Google Scholar 

  5. K. Itô and M. Nisio, On the convergence of sums of independent Banach space valued random variables. Osaka J. Math. 5 (1968), 35–48.

    MathSciNet  MATH  Google Scholar 

  6. A. Jakubowski, On the Skorokhod topology. Ann. Inst. H. Poincaré Probab. Statist. 22, (1986), 263–285.

    MathSciNet  MATH  Google Scholar 

  7. O. Kallenberg, Series of random processes without discontinuities of the second kind. Ann. Probab. 2 (1974), 729–737.

    Article  MathSciNet  MATH  Google Scholar 

  8. O. Kallenberg, Foundations of Modern Probability. 2nd Edition, Probability and its Applications. New York:S pringer-Verlag, 2002.

    Google Scholar 

  9. S. Kwapień and W.A. Woyczyński, Random Series and Stochastic Integrals: Single and Multiple. Probability and its Applications. Boston:Birk häuser Boston Inc., 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andreas Basse-O’Connor .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Basel

About this paper

Cite this paper

Basse-O’Connor, A., Rosiński, J. (2013). On Lévy’s Equivalence Theorem in Skorohod Space. In: Houdré, C., Mason, D., Rosiński, J., Wellner, J. (eds) High Dimensional Probability VI. Progress in Probability, vol 66. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0490-5_14

Download citation

Publish with us

Policies and ethics