Skip to main content
SpringerLink
Log in

On convergence of multiparameter strong submartingales in Banach lattices

О сходимости многопа раметрических сильн ых субмартингалов в банаховых решетках

  • Published:
Analysis Mathematica Aims and scope Submit manuscript

Abstract

В работе исследуются многопараметрическ ие субмартингалы со зна чениями в банахо-вых пространствах, сильн ые мартингалы и сильн ые субмартингалы.

Установлено, что еслиB - банахово пространс тво со свойством Радона—Ни кодима, то любойB-зяачный рав номерно интегрируем ый сильный мартингал {M n ,n∈N d} почти наверное сходится пр иn→∞.

С помощью этой теорем ы изучается сходимос ть сильных субмартингалов со зн ачениями в банаховой решетке.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Cairoli, R., Une inégalité pour martingales à indices multiples et ses applications. Seminaire de probabilités IV, Université de Strasbourg,Lecture Notes in Math.,124, 1–27; Springer (Berlin-Heidelberg-New York, 1970).

    Google Scholar 

  2. Chatterji, S. D., Vector-valued martingales and their applications. Probability in Banach Spaces, Oberwolfach,Lecture Notes in Math.,526, 33–51; Springer (Berlin-Heidelberg-New York, 1976).

    Google Scholar 

  3. Dozzi, M., On the decomposition and integration of two-parameter stochastic processes. Processus aléatoires à deux indices, Paris,Lecture Notes in Math.,863, 162–171; Springer (Berlin-Heidelberg-New York, 1981).

    Google Scholar 

  4. Fazekas, I., Convergence of vector-valued martingales with multidimensional indices. (To be published inPubl. Math. Debrecen).

  5. Millet, A., Convergence and regularity of strong submartingales. Processus aléatoires à deux indices, Paris,Lecture Notes in Math.,863, 50–58; Springer (Berlin-Heidelberg-New York, 1981).

    Google Scholar 

  6. Neveu, J.,Discrete-Parameter Martingales, North-Holland (Amsterdam-Oxford, 1975).

    Google Scholar 

  7. Nielsen, N. J., On Banach ideals determined by Banach lattices and their applications,Dissertationes Math.,109 (1973), 1–66.

    Google Scholar 

  8. Szulga, J., Regularity of Banach lattice valued martingales,Colloquium Math.,49 (1979), 303–312.

    Google Scholar 

  9. Szulga, J. andWoyczynski, W. A., Convergence of submartingales in Banach lattices,Ann. Probability,4 (1976), 464–469.

    Google Scholar 

  10. Walsh, J. B., Convergence and regularity of multiparameter strong martingales,Z. Wahrscheinlichkeitstheorie verw. Gebiete,46 (1979), 177–192.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kossuth Lajos University, 4010, Debrecen PF. 12, Hungary

    István Fazekas

Authors
  1. István Fazekas
    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

Fazekas, I. On convergence of multiparameter strong submartingales in Banach lattices. Analysis Mathematica 10, 207–212 (1984). https://doi.org/10.1007/BF01917634

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01917634

Keywords

Search

Navigation