Advertisement

On a problem of necessary and sufficient conditions in the functional central limit theorem for local martingales

  • R. Sh. Liptser
  • A. N. Shiryaev
Article

Keywords

Stochastic Process Probability Theory Limit Theorem Mathematical Biology Central Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aalen, O.: A model for nonparametric regression analysis of counting processes. Lecture Notes in Math. Math. Statist. and Probab. Theory, Proc Sixth. Intern. Conf. Wisła (Poland), 1–25 (1978)Google Scholar
  2. 2.
    Billingsly, P.: Convergence of probability measures. New York: Wiley 1968Google Scholar
  3. 3.
    Gänssler, P., Häusler, E.: Remarks on the functional central limit theorem for martingales. Z. Wahrscheinlichkeitstheorie verw. Gebiete 50, 237–243 (1979)Google Scholar
  4. 4.
    Jacod, J.: Calcul stochastique et problémes de martingales. Lecture Notes in Math. 714. Berlin-Heidelberg-New York: Springer 1979Google Scholar
  5. 5.
    Jacod, J.: Convergence en loi de semimartingales et variation quadratique. Seminaire de Probabilities XV; Lecture Notes in Math. 850, 547–560. Berlin-Heidelberg-New York: Springer (1979/1980)Google Scholar
  6. 6.
    Kabanov, Ju.M., Lipster, R.Sh., Shiryaev, A.N.: Absolute continuity and singularity of locally absolutely continuous probability distributions I. Math. USSR Sb. 35, 631–680 (1979)Google Scholar
  7. 7.
    Lipster, R.Sh., Shiryaev, A.N.: The functional central limit theorem for semimartingales. Theory Probab. Appl. XXV, 681–703 (1980)Google Scholar
  8. 8.
    Lipster, R.Sh., Shiryaev, A.N.: On necessary and sufficient conditions in functional central limit theorem for semimartingales. Theory Probab. Appl. XXVI, 132–137 (1981)Google Scholar
  9. 9.
    McLeish, D.L.: An extended martingale principle. Ann Probab. 6, 144–150 (1978)Google Scholar
  10. 10.
    Rebolledo, R.: Sur le théoréme de a limite central pour les martingales. C.R. Acad. Sci. Paris Sér., A288, 879–882 (1979)Google Scholar
  11. 11.
    Rebolledo, R.: The central limit theorem for semimartingales: necessary and sufficient conditions. Z. Wahrscheinlichkeitstheorie verw. Gebiete (1981); preprintGoogle Scholar
  12. 12.
    Rootzen, H.: On the functional central limit theorem for martingales, I, II. Z. Wahrscheinlichkeitstheorie verw. Gebiete 38, 199–210 (1977); 51, 77–93 (1980)Google Scholar
  13. 13.
    Stone, C.: Weak convergence of stochastic processes defined on semi-finite time intervals. Proc. Amer. Math. Soc. 694–696 (1963)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • R. Sh. Liptser
    • 1
  • A. N. Shiryaev
    • 2
  1. 1.Institute of Control ScienceMoscowUSSR
  2. 2.Steclov Mathematical InstituteMoscowUSSR

Personalised recommendations