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Integrals, conditional expectations, and martingales of multivalued functions

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Cited by:

  1. Fabián Flores-Bazán & Luis González-Valencia, 2021. "Characterizing Existence of Minimizers and Optimality to Nonconvex Quadratic Integrals," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 497-522, February.
  2. Wang, JinRong & Ibrahim, Ahmed Gamal & Fečkan, Michal, 2015. "Nonlocal impulsive fractional differential inclusions with fractional sectorial operators on Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 103-118.
  3. Jérôme Couvreux & Christian Hess, 1999. "A Lévy Type Martingale Convergence Theorem for Random Sets with Unbounded Values," Journal of Theoretical Probability, Springer, vol. 12(4), pages 933-969, October.
  4. Weixuan Xia, 2023. "Optimal Consumption--Investment Problems under Time-Varying Incomplete Preferences," Papers 2312.00266, arXiv.org.
  5. Tuan Nguyen Dinh, 2023. "Regularity of Multipliers for Multiobjective Optimal Control Problems Governed by Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 762-796, February.
  6. Johan Jonasson, 1998. "On Positive Random Objects," Journal of Theoretical Probability, Springer, vol. 11(1), pages 81-125, January.
  7. Asgar Jamneshan & Michael Kupper & José Miguel Zapata-García, 2020. "Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 644-666, August.
  8. Reza Ezzati & Shokrollah Ziari, 2012. "Approximation of fuzzy integrals using fuzzy bernstein polynomials," Fuzzy Information and Engineering, Springer, vol. 4(4), pages 415-423, December.
  9. Guillermo Ayala & María Concepción López-Díaz & Miguel López-Díaz & Lucía Martínez-Costa, 2015. "Methods and Algorithms to Test the Hausdorff and Simplex Dispersion Orders with an R Package," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 661-675, September.
  10. Emmanuel Lepinette & Ilya Molchanov, 2016. "Risk Arbitrage and Hedging to Acceptability under Transaction Costs," Papers 1605.07884, arXiv.org, revised Apr 2020.
  11. Kim, Taesung & Yannelis, Nicholas C., 1997. "Existence of Equilibrium in Bayesian Games with Infinitely Many Players," Journal of Economic Theory, Elsevier, vol. 77(2), pages 330-353, December.
  12. Li Guan & Juan Wei & Hui Min & Junfei Zhang, 2021. "The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
  13. Meriam El Mansour & Emmanuel Lépinette, 2020. "Conditional Interior and Conditional Closure of Random Sets," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 356-369, November.
  14. Bhowmik, Anuj, 2013. "Edgeworth equilibria: separable and non-separable commodity spaces," MPRA Paper 46796, University Library of Munich, Germany.
  15. Yan Sun & Guanghua Lian & Zudi Lu & Jennifer Loveland & Isaac Blackhurst, 2020. "Modeling the Variance of Return Intervals Toward Volatility Prediction," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 492-519, July.
  16. Weixuan Xia, 2023. "Set-valued stochastic integrals for convoluted L\'{e}vy processes," Papers 2312.01730, arXiv.org, revised Aug 2024.
  17. Kosaku Takanashi, 2017. "Local Asymptotic Normality of Infinite-Dimensional Concave Extended Linear Models," Keio-IES Discussion Paper Series 2017-012, Institute for Economics Studies, Keio University.
  18. Terán, Pedro, 2003. "A strong law of large numbers for random upper semicontinuous functions under exchangeability conditions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 251-258, November.
  19. Pennanen, Teemu & Perkkiö, Ari-Pekka, 2018. "Convex integral functionals of regular processes," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1652-1677.
  20. Wolfgang Näther & Andreas Wünsche, 2007. "On the Conditional Variance of Fuzzy Random Variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(1), pages 109-122, February.
  21. M. Guo & X. Xue & R. Li, 2004. "Controllability of Impulsive Evolution Inclusions with Nonlocal Conditions," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 355-374, February.
  22. Wang, Rongming & Wang, Zhenpeng, 1997. "Set-Valued Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 180-198, October.
  23. López-Diaz, Miguel & Gil, Maria Angeles, 1997. "Constructive definitions of fuzzy random variables," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 135-143, December.
  24. Pascal Bianchi & Walid Hachem, 2016. "Dynamical Behavior of a Stochastic Forward–Backward Algorithm Using Random Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 90-120, October.
  25. Ilya Molchanov & Anja Mühlemann, 2021. "Nonlinear expectations of random sets," Finance and Stochastics, Springer, vol. 25(1), pages 5-41, January.
  26. Castaing, Charles & Quang, Nguyen Van & Thuan, Nguyen Tran, 2012. "A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 84-95.
  27. De Simone, Anna & Graziano, Maria Gabriella, 2003. "Cone conditions in oligopolistic market models," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 53-73, February.
  28. López-Díaz, Miguel, 2006. "An indexed multivariate dispersion ordering based on the Hausdorff distance," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1623-1637, August.
  29. Rodríguez-Muñiz, Luis J. & López-Díaz, Miguel, 2007. "On the exchange of iterated expectations of random upper semicontinuous functions," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1628-1635, October.
  30. Mariusz Michta & Jerzy Motyl, 2022. "Set-Valued Functions of Bounded Generalized Variation and Set-Valued Young Integrals," Journal of Theoretical Probability, Springer, vol. 35(1), pages 528-549, March.
  31. Emmanuel Lepinette, 2020. "Random optimization on random sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 159-173, February.
  32. Tourky, Rabee & Yannelis, Nicholas C., 2001. "Markets with Many More Agents than Commodities: Aumann's "Hidden" Assumption," Journal of Economic Theory, Elsevier, vol. 101(1), pages 189-221, November.
  33. Emmanuel Lepinette & Ilya Molchanov, 2017. "Conditional cores and conditional convex hulls of random sets," Papers 1711.10303, arXiv.org.
  34. Ezzaki, Fatima & Tahri, Khalid, 2019. "Representation theorem of set valued regular martingale: Application to the convergence of set valued martingale," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
  35. Emmanuel Lépinette & Ilya Molchanov, 2021. "Risk arbitrage and hedging to acceptability under transaction costs," Finance and Stochastics, Springer, vol. 25(1), pages 101-132, January.
  36. Ilya Molchanov & Anja Muhlemann, 2019. "Nonlinear expectations of random sets," Papers 1903.04901, arXiv.org.
  37. Tito Homem-de-Mello, 2001. "Estimation of Derivatives of Nonsmooth Performance Measures in Regenerative Systems," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 741-768, November.
  38. Jinping Zhang & Keming Zhang, 2022. "Portfolio selection models based on interval-valued conditional value at risk (ICVaR) and empirical analysis," Papers 2201.02987, arXiv.org, revised Jul 2022.
  39. Charles Castaing & Christiane Godet-Thobie & Le Xuan Truong, 2020. "Fractional Order of Evolution Inclusion Coupled with a Time and State Dependent Maximal Monotone Operator," Mathematics, MDPI, vol. 8(9), pages 1-30, August.
  40. Ayala, Guillermo & López-Díaz, Miguel, 2009. "The simplex dispersion ordering and its application to the evaluation of human corneal endothelia," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1447-1464, August.
  41. Teemu Pennanen, 2011. "Convex Duality in Stochastic Optimization and Mathematical Finance," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 340-362, May.
  42. Henry, Marc, 2007. "A representation of decision by analogy," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 771-794, September.
  43. Lopez-Diaz, Miguel & Rodriguez-Muniz, Luis J., 2007. "Influence diagrams with super value nodes involving imprecise information," European Journal of Operational Research, Elsevier, vol. 179(1), pages 203-219, May.
  44. Jang, Lee-Chae & Kwon, Joong-Sung, 1998. "A uniform strong law of large numbers for partial sum processes of Banach space-valued random sets," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 21-25, May.
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