Adv. Math. Econ. 14, 1-34 (2010)

Some various convergence results for multivalued martingales

Fettah Akhiat^{1}, Charles Castaing^{2} and Fatima Ezzaki ^{3}

1 Laboratoire modélisation et calcul scientifique, Département de Mathématiques, Faculté des Sciences et Techniques, BP 2202, Fès Maroc (akhiatfettah@yahoo.fr)

2 Département de Mathématiques, Université Montpellier II, 34095 Montpellier Cedex 5, France (castaing.charles@numericable.fr)

3 Laboratoire modélisation et calcul scientifique, Département de Mathématiques, Faculté des Sciences et Techniques, BP 2202, Fès Maroc (fatimaezzaki@yahoo.fr)

Received: April 26, 2009 Revised: October 15, 2009

JEL classification: C01, C02, G12

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

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.

Key words: martingale, submartingale, supermartingale, mil, conditional expectation, Mosco convergence, linear topology, Pettis.