참고문헌
- F. Akhiat, C. Castaing and F. Ezzaki, Some various convergence results for multivalued martingales, Adv. Math. Econ. 13 (2010), 1-33. https://doi.org/10.1007/978-4-431-99490-9_1
- N. Bourbaki, Elements de mathematiques, Topologie Generale, Chaps. 1-4, Hermann, Paris. 1971.
- C. Castaing, F. Ezzaki, M. Lavie, and M. Saadoune, Weak star convergence of martin-gales in a dual space, Function spaces IX, 45-73, Banach Center Publ., 92, Polish Acad. Sci. Inst. Math., Warsaw, 2011.
- C. Castaing, F. Ezzaki, and K. Tahri, Convergence of multivalued pramarts, J. Nonlinear Convex Anal. 11 (2010), no. 2, 243-266.
- C. Castaing and M. Saadoune, Convergences in a dual space with applications to Fatou lemma, Adv. Math. Econ. 12 (2009), 23-69. https://doi.org/10.1007/978-4-431-92935-2_2
- C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lectures Notes, 580, Springer-Verlag, Berlin 1977.
- A. Choukairi-Dini, M-convergence, et regularite des martingales multivoques: epimartingales, J. Multivariate Anal. 33 (1990), no. 1, 49-71. https://doi.org/10.1016/0047-259X(90)90005-3
- A. Choukairi-Dini, On almost sure convergence of vector valued pramarts and multivalued pramarts, J. Convex Anal. 3 (1996), no. 2, 245-254.
- L. Egghe, Stopping time techniques for analysts and probabilists, Cambridge Univ. Press, London and New York, 1984.
- L. Egghe,, Strong convergence of pramarts in Banach spaces, Canad. J. Math. 33 (1981), no. 2, 357-361. https://doi.org/10.4153/CJM-1981-029-8
- C. Hess, On multivalued martingales whose values may be unbounded: martingale selectors and Mosco convergence, J. Multivariate Anal. 39 (1991), no. 1, 175-201. https://doi.org/10.1016/0047-259X(91)90012-Q
- F. Hiai and H. Umegaki, Integrals, conditional expectations and martingales of multi- valued functions, J. Multivariate Anal. 7 (1977), no. 1, 149-182. https://doi.org/10.1016/0047-259X(77)90037-9
- S. Li and Y. Ogura, Convergnece of set valued sub-and supermartingales in the Kuratowski-Mosco sense, Ann. Prob. 26 (1998), no. 3, 1384-1402. https://doi.org/10.1214/aop/1022855757
- D. Q. Lu'u, Representations and regularity of multivalued martingales, Acta Math. Vietnam. 6 (1981), no. 2, 29-40.
- D. Q. Lu'u, On convergence of multivalued asymptotic martingales, Seminaire d'analyse convexe, Vol. 14 (Montpellier, 1984), Exp. No. 5, 23 pp., Univ. Sci. Tech. Languedoc, Montpellier, 1984.
- D. Q. Lu'u, Representations of multivalued (regular) uniform amarts, Seminaire d'analyse convexe, Vol. 14 (Montpellier, 1984), Exp. No. 9, 33 pp., Univ. Sci. Tech. Languedoc, Montpellier, 1984.
- J. Neveu, Convergence presque sˆur de martingales multivoques, Ann. Inst. H. Poincare Sect. B (N.S.) 8 (1972), no. 1, 1-7.
- M. Valadier, On conditional expectation of random sets, Ann. Mat. Pura Appl. (4) 126 (1980), 81-91. https://doi.org/10.1007/BF01762501
- Z. P. Wang and X. H. Xue, On convergence and closedness of multivalued martingales, Trans. Amer. Math. Soc. 341 (1994), no. 2, 807-827. https://doi.org/10.1090/S0002-9947-1994-1154544-X
- Z. P. Wang and X. H. Xue, Some remarks on pramarts and mils, Glasg. Math. J. 35 (1993), no. 2, 239-251. https://doi.org/10.1017/S0017089500009800