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Some various convergence results for multivalued martingales

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Advances in Mathematical Economics

Part of the book series: Advances in Mathematical Economics ((MATHECON,volume 13))

Abstract

We prove various convergence results for multivalued martingales, sub- supermartingales and mils with respect to the Mosco topology and the linear topology both in Bochner integration and Pettis integration. We also state some existence theorems of Pettis conditional expectation for multivalued Pettis-integrable multifunctions.

Received: April 26, 2009

Revised: October 15, 2009

JEL classification: C01, C02, G12

Mathematics Subject Classification (2000): 28B20, 60G42, 46A17, 54A20

We heartily thank the referee for helpful comments and suggestions.

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Authors and Affiliations

  1. Laboratoire modélisation et calcul scientifique, Département de Mathématiques, Faculté des Sciences et Techniques, Université Sidi Mohamed Ben Abdellah, BP 2202, Fes, Morocco

    Fettah Akhiat & Fatima Ezzaki

  2. Département de Mathématiques, Université Montpellier II, 34095, Montpellier Cedex 5, France

    Charles Castaing

Authors
  1. Fettah Akhiat
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  2. Charles Castaing
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  3. Fatima Ezzaki
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Correspondence to Fatima Ezzaki .

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Editors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-0041, Japan

    Shigeo Kusuoka (Professor) (Professor)

  2. Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan

    Toru Maruyama (Professor) (Professor)

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Akhiat, F., Castaing, C., Ezzaki, F. (2010). Some various convergence results for multivalued martingales. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 13. Springer, Tokyo. https://doi.org/10.1007/978-4-431-99490-9_1

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