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
Extended convergence to continuous in probability processes with independent increments
Download PDF
Download PDF
  • Published: April 1986

Extended convergence to continuous in probability processes with independent increments

  • Adam Jakubowski1 &
  • Leszek Słomiński1 

Probability Theory and Related Fields volume 72, pages 55–82 (1986)Cite this article

  • 132 Accesses

  • 8 Citations

  • Metrics details

Summary

A special (“extended”) kind of convergence in distribution of processes with filtration is considered. Recent theorems on the functional convergence of semimartingales are improved by showing that their assumptions imply the extended convergence of semimartingales to continuous in probability processes with independent increments.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Aldous, D.J.: Stopping times and tightness. Ann. Probab. 6, 335–340 (1978)

    Google Scholar 

  2. Aldous, D.J.: A concept of weak convergence for stochastic processes viewed in the Strasbourg manner. Preprint, Statist. Laboratory, Univ. Cambridge (1979)

  3. Bilingsley, P.: Weak Convergence of Probability Measures. New York: Wiley 1968

    Google Scholar 

  4. Grigelionis, B.: On the martingale characterization of stochastic processes with independent increments. Lietuwos Matematikos Rinkinys XVII, N0 1, 75–86 (1977)

    Google Scholar 

  5. Helland, I.S.: On Weak Convergence to Brownian Motion. Z. Wahrscheinlichkeitstheor. Verw. Gebiete 52, 251–265 (1980)

    Google Scholar 

  6. Ikeda, N., Watanabe, S.: Stochastic Differential Equation and Diffusion Processes. Amsterdam-Oxford-New York: North-Holland Publishing Company 1981

    Google Scholar 

  7. Jacod, J.: Calcul stochastique et problèmes de martingales. Lecture Notes in Math., N0 714. Berlin-Heidelberg-New York: Springer 1979

    Google Scholar 

  8. Jacod, J.: Processus à accroissements indépendants: une condition nécessaire et suffisante de convergence en loi. Z. Wahrscheinlichkeitstheor. Verw. Gebiete 63, 109–136 (1983)

    Google Scholar 

  9. Jacod, J., Kłopotowski, A., Memin, J.: Théorème de la limite centrale et convergence fonctionnelle vers un processus à accroissements indépendants: la méthode des martingales. Ann. I.H.P., XVIII, N0 1, 1–45 (1982)

    Google Scholar 

  10. Jakubowski, A.: Limit theorems for sums of dependent random variables with values in a Hilbert space. Thesis, (in Polish) Toruń, (1982)

  11. Lindvall, T.: Weak convergence of probability measures and random functions in the function space D [0, ∞]. J. Appl. Probab. 10, 109–121 (1973)

    Google Scholar 

  12. Liptser, R., Shiryaev, A.: Necessary and sufficient conditions for the functional central limit theorem for semimartingales. Theory Probab. Appl. 26, 132–137 (1981)

    Google Scholar 

  13. Liptser, R., Shiryaev, A.: On a Problem of Necessary and Sufficient Conditions in the Functional Central Limit Theorem for Local Martingales. Z. Wahrscheinlichkeitstheor. Verw. Gebiete 59, 311–318 (1982)

    Google Scholar 

  14. Słomiński, L.: Necessary and sufficient conditions for extended convergence of semimartingales. Preprint (1984)

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Nicholas Copernicus University, ul. Chopina 12/18, PL-87-100, Toruń, Poland

    Adam Jakubowski & Leszek Słomiński

Authors
  1. Adam Jakubowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leszek Słomiński
    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

Jakubowski, A., Słomiński, L. Extended convergence to continuous in probability processes with independent increments. Probab. Th. Rel. Fields 72, 55–82 (1986). https://doi.org/10.1007/BF00343896

Download citation

  • Received: 05 November 1983

  • Revised: 10 May 1985

  • Issue Date: April 1986

  • DOI: https://doi.org/10.1007/BF00343896

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

  • Filtration
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Probability Process
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