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Acta Mathematicae Applicatae Sinica

, Volume 4, Issue 2, pp 136–144 | Cite as

On local comparability among families of sub-σ-fields

  • Chen Peide 
  • Zhuang Xingwu 
Article
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Abstract

In this paper, we discuss some basic properties of local comparability, extend the main results of [1] from the case of two-parameter to the case ofm-parameter (m any positive integer). We also discuss local comparability in families of sub-σ-fields indexed by Riesz space and its application.

Keywords

Positive Integer Basic Property Math Application Riesz Space Local Comparability 
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.

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References

  1. [1]
    Gheorghita ZbĂganu & Zhuang Xing-wu, Two-Parameter Filtration with Respect to which All Martingales are Strong,Z. Wahrscheinlichkeitstheoris verw. Gebiete61 (1982), 437–452.Google Scholar
  2. [2]
    Cairoli, R. & Walsh, J. B., Stochastic Integrals in the Plane,Acta Math.,134 (1975), 111–183.Google Scholar
  3. [3]
    Zhuang Xin-wu & Chen Pei-de, On the Conditional Independence.Jour. of Fujian Normal University, 1 (1984), 23–30.Google Scholar
  4. [4]
    Chen Pei-de, Supermartingales and Dual-supermartingales Indexed by Riesz Space,Jour. of Fujian Normal University, 1 (1984), 9–22.Google Scholar
  5. [5]
    Yan Jia-an: On the Martingale and Stochastic Integral, Shanghai Science and Technology Publishing House (in Chinese), 1981.Google Scholar
  6. [6]
    Walsh, J. B., Martingales with a Multi-dimensional Parameter and Stochastic Integrals in the Plane, Cours. 3e, Cycle. Univ., Paris VI (1977).Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc. New York, U.S.A. 1988

Authors and Affiliations

  • Chen Peide 
    • 1
  • Zhuang Xingwu 
    • 2
  1. 1.Institute of Applied Mathematics, Academia SinicaChina
  2. 2.Fujian Normal UniversityChina

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