논문KCI 등재
Conditional expectation of Pettis integrable unbounded random sets
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this paper we established new results of existence of conditional expectation for closed convex and unbounded Pettis integrable random sets without assuming the Radon Nikodym property of the Banach space. As application, new versions of multivalued L\'evy's martingale convergence theorem are proved by using the Slice and the linear topologies.
Abstract
In this paper we established new results of existence of conditional expectation for closed convex and unbounded Pettis integrable random sets without assuming the Radon Nikodym property of the Banach space. As application, new versions of multivalued L\'evy's martingale convergence theorem are proved by using the Slice and the linear topologies.
참고문헌 (28)
- F. Akhiat, "Some various convergence results for multival-ued martingales", Advances in Mathematical Economics, 13, pp.1~33 (2010), Springer[DOI]
- Fattah Akhiat, "Pettis conditional expectation of closed convex random sets in a Banach space without $RNP$", 대한수학회지, 55(4), pp.833~848 (2018), 대한수학회
- A. Amrani, "Weak compactness in Pettis integration", Bull. Polish Acad. Sci. Math, 45(2), pp.139~150 (1997)
- I. Assani, "Parties decomposables compactes de L1E", C. R. Acad. Sci. Paris Ser. I Math, 294(16), pp.533~536 (1982)
- G. Beer, "Support and distance functionals for convex sets", Numer. Funct. Anal. Optim, 10(1-2), pp.15~36 (1989)[DOI]
- C. Castaing, "Convex analysis and measurable multifunctions", Lecture Notes in Mathematics, 580 (1977), Springer-Verlag
- N. D. Chakraborty, "Convergence theorems for Pettis integrable func-tions and regular methods of summability", J. Math. Anal. Appl, 359(1), pp.95~105 (2009)[DOI]
- S. D. Chatterji, "Martingales of Banach-valued random variables", Bull. Amer. Math. Soc, 66, pp.395~398 (1960)[DOI]
- A. Choukairi, "Sur la convergence d'esperances conditionnelles de multiapplications", Seminaire d'analyse convexe, 17, pp.19~ (1987)
- W. Dong, "On representation and regularity of continuous parame-ter multivalued martingales", Proc. Amer. Math. Soc, 126(6), pp.1799~1810 (1998)[DOI]
- R. M. Dudley, "Cam-bridge Studies in Advanced Mathematics, 74" (2002), Cambridge University Press
- K. El Amri, "On the Pettis integral of closed valued multifunctions", Set-Valued Anal, 8(4), pp.329~360 (2000)[DOI]
- M. El Harami, "General Pettis conditional expectation and convergence theorems", Int. J. Math. Stat, 11(1), pp.91~111 (2012)
- F. Ezzaki, "Convergence des esperances conditionnelles d'ensembles aleatoires et LFGN", Doctor, Faculte des Sciences, pp.1996
- A. Faik, "Contribution a l'analyse des multifonctions et a l'etude de quelques problemes d'evolution", Doctor, pp.1995
- C. Godet-Thobie, "Decomposability and uniform integrability in Pet-tis integration", Quaest. Math, 29(1), pp.39~58 (2006)[DOI]
- C. Hess, "Quelques resultats sur la mesurabilite des multifonctions a valeurs dans un espace metrique separable", Seminaire d'analyse convexe, 16(1), pp.43~ (1986), Univ. Sci. Tech
- C. Hess, "Measurability and integrability of the weak upper limit of a sequence of multi-functions", J. Math. Anal. Appl, 153(1), pp.226~249 (1990)[DOI]
- F. Hiai, "Integrals, conditional expectations, and martingales of multi-valued functions", J. Multivariate Anal, 7(1), pp.149~182 (1977)[DOI]
- G. Krupa, "Convergence of unbounded multivalued supermartingales in the Mosco and slice topologies", J. Convex Anal, 5(1), pp.187~198 (1998)
- K. Musia l, "General topology and its relations to modern analysis and algebra, IV", pp.308~310 (1977), Soc. Czechoslovak Mathematicians and Physicists
- K. Musial, "The weak Radon-Nikodym property in Banach spaces", Studia Math, 64(2), pp.151~174 (1979)[DOI]
- J. Neveu, "Martingales a temps discret" (1972), Masson et Cie
- N. S. Papageorgiou, "Convergence theorems for set-valued conditional expectations, Com-ment", Math. Univ. Carolin, 34(1), pp.97~104 (1993)
- M. Talagrand, "Pettis integral and measure theory", Mem. Amer. Math. Soc., 51(307), pp.9~ (1984)[DOI]
- Z. P. Wang, "On convergence and closedness of multivalued martingales", Trans. Amer. Math. Soc, 341(2), pp.807~827 (1994)[DOI]
- X. Xue, "Set valued measures and integral representation", Comment. Math. Univ. Carolin, 37(2), pp.269~284 (1996)
- H. Ziat, "Convergence des suites adaptees multivoques application a la loi forte des grands nombres multivoque", Doctor, pp.1993
관련 논문AI추천
Pettis conditional expectation of closed convex random sets in a Banach space without $RNP$Fatima Ezzaki, Fattah Akhiat, Mohamed El Harami대한수학회 · 대한수학회지2018 · 제55권 제4호Representation theorems for multivalued pramartsFatima Ezzaki, Fettah Akhiat대한수학회 · 대한수학회지2013 · 제50권 제1호SET-VALUED CHOQUET-PETTIS INTEGRALS박춘기강원경기수학회 · 한국수학논문집2012 · 제20권 제4호Convergence theorems for the Choquet-Pettis integral박춘기강원경기수학회 · 한국수학논문집2014 · 제22권 제2호Some notes on strong law of large numbers for Banach space valued fuzzy random variables김윤경, 김주목강원경기수학회 · 한국수학논문집2013 · 제21권 제4호Convergence theorems for set-valued Denjoy-Pettis integrable mappingsChun-Kee Park대한수학회 · 대한수학회논문집2009 · 제24권 제2호
이 간행물의 다른 논문 (13건)
Modular Jordan type for $\k [x, y] / (x^m,y^n)$ for $m = 3, 4$신용수, 박정필pp. 283-312Harnack estimates for nonlinear backward heat equations with potentials along the Ricci-Bourguignon flowJian-Hong Wangpp. 313-329Applications of differential subordinations to certain classes of starlike functionsShagun Banga, S. SIVAPRASAD KUMARpp. 331-357Orbit equivalence on self-similar groups and their $C^*$-algebras이인협pp. 383-399An efficient algorithm for sliding window based incremental principal components analysis이근섭pp. 401-414
