On multivalued supermartingales with continuous parameter:martingale selectors and their regularity

References

• Bagchi , S. 1985 . On a.s. convergence of classes of multiualued asymptotic martingales . Ann. Inst. Henri Poincare , 21 : 313 – 321 .
   Google Scholar
• Beer , G. 1989 . Convergence of continuous linear [unctionals and their level sets . Arch. Math , 52 : 482 – 491 .
   Google Scholar
• Beer , G. 1989 . Support and distance functionals for convex sets . Number. Funct. Anal. and Optimiz. , 10 : 15 – 36 .
   Web of Science ®Google Scholar
• Castaing , C. and Valadier , M. 1977 . Lecture Notes in Math , Vol. 580 , Berlin : Springer-Verlag .
   Google Scholar
• Chacon , R.V. and Sucheston , L. 1975 . On convergence of vector valued asymptotic martingales, Z . Wahrs. verw. Gebiete , 33 : 55 – 59 .
   Google Scholar
• Chatterji , S. 1976 . “ Vector ualues martingales and their applications ” . In Lecture Notes in Math , Vol. 526 , 33 – 51 . Berlin, New York : Springer-Verlag .
   Google Scholar
• Choi , B. and Sucheston , L. 1981 . “ Continuous parameter uniform am arts ” . In Lecture Notes in Math , Vol. 860 , 85 – 98 . Berlin : Springer-Verlag .
   Google Scholar
• Daures , J.P. 1973 . Version multiuoque du théoréme de Doob . Ann. Inst. Henri Poincaré , 860 : 167 – 176 .
   Google Scholar
• Dellacherie , C. and Meyer , P.A. 1982 . Probabilities and potentials B , Vol. VI , Netherlands : NorthHolland .
   Google Scholar
• Egghe , L. 1981 . Strong convergence of pram arts in Banach paces . Cando J. Math , 33 : 357 – 361 .
   Google Scholar
• Frangos , N.E. 1985 . On regularity of Banach-valued processes . Ann. Prob , 13 ( 3 ) : 985 – 990 .
   Web of Science ®Google Scholar
• Frangos , N.E. 1985 . On convergence of vector valued pram aris and subpramarts . Canad. J. Math , 37 ( 3 ) : 260 – 270 .
   Google Scholar
• Giné , E. , Hahn , M.G. and Zinn , J. 1983 . “ Limit theorems for random sets:An application of probability in Banach space results ” . In Lecture Notes in Math , Vol. 990 , 112 – 135 . Berlin, New York : Springer-Verlag .
   Google Scholar
• Gut , A. and Schmidt , K.D. 1983 . “ Amarts and set function processes ” . In Lecture Notes in Math , Vol. 1042 , Berlin, New York : Springer- Verlag .
   Google Scholar
• Hess , C. 1991 . On multivalued martingales whose ualues may be unbounded:martingale selectors and Mosco convergence . J .Multivariate Anal , 39 : 175 – 201 .
   Web of Science ®Google Scholar
• Hess , C. August 1991 . “ Convergence of conditional expectations for unbounded random sets] integrals, and integrals [unctio nals ” . In Math. Oper. Res Vol. 16 , August , 627 – 649 .
   Google Scholar
• Hess , C. 1991 . Existence of martingale selectors and convergence of'1nultivai'ued supermartingales . C.R.Acad. Sci. Paris Ser. I Math , 312 ( 1 ) August : 149 – 154 .
   Google Scholar
• Hiai , F. and Umegaki , H. 1977 . Integrals, conditional expectations, and martingales of multivalued functions . J.Multivariate Anal , 7 ( 1 ) August : 149 – 182 .
   Web of Science ®Google Scholar
• Hiai , F. 1985 . Convergence of conditional expectations and strong laws of large numbers for multivalued random variables . Trans. Ameri. Math. Soc , 291 ( 2 ) August : 613 – 627 .
   Web of Science ®Google Scholar
• Luu , D.Q. 1985 . Representations and regularity of multivalued martingales . C.R. Acad. Sci. Serie , 1300 ( 2 ) August : 63 – 65 .
   Google Scholar
• Millet , A. and Sucheston , L. 1979 . Characterizations of Vitali Conditions with overlap in terms of convergence of amarts . Canad. J. Math , 31 ( 2 ) August : 1033 – 1046 .
   Google Scholar
• Millet , A. and Sucheston , L. 1980 . Convergence of classes of «m arts indexed by directed Sets . Canad. J. Math , 32 ( 2 ) August : 86 – 125 .
   Google Scholar
• Papageorgiou , N.S. 1985 . On the theory of Banach space val'ued multifunctions,l. Integration and conditional expectation . J .Multivariate Anal , 17 ( 2 ) August : 185 – 206 .
   Web of Science ®Google Scholar
• Papageorgiou , N.S. 1985 . On the theory of Banach space valued 'm'ultifunctions,2 Set valued martingales and set valued measures . J .Multivariate Anal , 17 ( 2 ) August : 207 – 227 .
   Web of Science ®Google Scholar
• Papageorgiou , N.S. 1987 . Convergence theorems for Banach space valued integrable multi/unctions . Intern. J .Math. & Math. Sci , 10 ( 2 ) August : 433 – 442 .
   Google Scholar
• Papageorgiou , N.S. 1987 . A convergence theorem for set-valued sapermurtinqale with values in a separable Banach space . Stach. Anal. AppL , 5 ( 2 ) August : 405 – 422 .
   Google Scholar
• Papageorgiou , N.S. 1989 . Convergence and representation theorems for set-valued . Stoch. Anal. Appl , 7 ( 2 ) August : 187 – 210 .
   Web of Science ®Google Scholar
• Salinetti , G. and Wets , R. 1977 . On the relations between two types of convergence for . J.Math.Anal.Appl. , 60 ( 2 ) August : 211 – 226 .
   Google Scholar
• Salinetti , G. and Wets , R. 1981 . On the convergence of closed-valued measurable multi/ Unctions . Trans. Amer. Math. Soc , 266 ( 2 ) August : 275 – 289 .
   Google Scholar
• Slaby , M. 1985 . Strong cotiuerqence of vector-valued pram arts and subprarnurts . Prob. Math. Statist , 5 ( 2 ) August : 187 – 190 .
   Google Scholar
• Tsukada , M. 1984 . Convergence of best approximations in a smooth Banach Space . J. Approx. Th , 40 ( 2 ) August : 301 – 309 .
   Google Scholar
• Wang , Z.P. 1987 . The laitice properties of martingale- like sequences . Acta Math. Sinica , 30 ( 2 ) August : 355 – 360 .
   Google Scholar
• Wang , Z.P. Martingale representation theorem for multivalued martingales with continuous parameters , Preprint .
   Google Scholar
• Wang , Z.P. and Xue , X.H. 1992 . Multivalued martingales, submartingales and supermartingales . Bulletin of Chinese Science , 24 ( 3 ) : 207 – 209 . Chinese
   Google Scholar
• Wang , Z.P. and Xue , X.H. 1994 . On convergence and closedness of multivalued martingales . Trans. Amer. Math. Soc , 341 ( 2 ) : 807 – 827 .
   Web of Science ®Google Scholar
• Yamasaki , Y. 1981 . Another convergence theorem of martingales in the limit . Tohoku Math. J , 33 ( 2 ) : 555 – 559 .
   Google Scholar