Uniform amarts: A class of asymptotic martingales for which strong almost sure convergence obtains

  • Alexandra Bellow


Stochastic Process Probability Theory Mathematical Biology Asymptotic Martingale 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Austin, D.G., Edgar, G.A., Ionescu Tulcea, A.: Pointwise convergence in terms of expectations. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 30, 17–26 (1974)Google Scholar
  2. 2.
    Bellow, A.: On vector-valued asymptotic martingales. Proc. nat. Acad. Sci. USA 73, No. 6, 1798–1799 (1976).Google Scholar
  3. 3.
    Bellow, A.: Several stability properties of the class of asymptotic martingales. Z. Wahrscheinlichkeitstheorie verw. Gebiete 37, 275–290 (1977)Google Scholar
  4. 4.
    Bellow, A.: Les amarts uniformes. C.R. Acad. Sci. Paris 284, Sér. A, 1295–1298 (1977)Google Scholar
  5. 5.
    Brunel, A., Sucheston, L.: Sur les amarts à valeurs vectorielles. C.R. Acad. Sci. Paris 283, Sér. A, 1037–1040 (1976)Google Scholar
  6. 6.
    Chacon, R.V.: A “stopped” proof of convergence. Advances in Math. 14, 365–368 (1974)Google Scholar
  7. 7.
    Chacon, R.V., Sucheston, L.: On convergence of vector-valued asymptotic martingales. Z. Wahrscheinlichkeitstheorie verw. Gebiete 33, 55–59 (1975)Google Scholar
  8. 8.
    Chatterji, S.D.: Martingale convergence and the Radon-Nikodym Theorem. Math. Scand. 22, 21–41 (1968)Google Scholar
  9. 9.
    Dunford, N., Schwartz, J.T.: Linear Operators. Part I. New York: Wiley 1953.Google Scholar
  10. 10.
    Edgar, G.A., Sucheston, L.: Amarts: A class of asymptotic martingales (Discrete parameter). J. multivariate Analysis 6, 193–221 (1976)Google Scholar
  11. 11.
    Edgar, G.A., Sucheston, L.: The Riesz decomposition for vectorvalued amarts. Z. Wahrscheinlichkeitstheorie verw. Gebiete 36, 85–92 (1976)Google Scholar
  12. 12.
    Fisk, D.L.: Quasi-martingales. Trans. Amer. math. Soc. 120, 369–389 (1965Google Scholar
  13. 13.
    Ionescu Tulcea, A., Ionescu Tulcea, C.: Abstract ergodic theorems. Trans. Amer. math. Soc. 107, 107–124 (1963)Google Scholar
  14. 14.
    Métivier, M.: Limites projectives de mesures; martingales; applications. Ann. Math. pura appl., IV Ser., 63, 225–252 (1963)Google Scholar
  15. 15.
    Neveu, J.: Martingales à Temps Discret. Paris: Masson 1972.Google Scholar
  16. 16.
    Orey, S.: F-Processes. Proc. 5th Berkeley Sympos. Math. Statist. Probab. II, pp. 301–313. Univ. of Calif, 1965/66Google Scholar
  17. 17.
    Rao, K.M.: Quasi-martingales. Math. Scand. 24, 79–92 (1969)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Alexandra Bellow
    • 1
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

Personalised recommendations