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Integrals, conditional expectations, and martingales of multivalued functions

Citations

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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. 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.
  5. 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.
  6. Emmanuel Lepinette & Ilya Molchanov, 2016. "Risk Arbitrage and Hedging to Acceptability under Transaction Costs," Papers 1605.07884, arXiv.org, revised Apr 2020.
  7. 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.
  8. 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.
  9. Weixuan Xia, 2023. "Set-valued stochastic integrals for convoluted L\'{e}vy processes," Papers 2312.01730, arXiv.org, revised Nov 2024.
  10. Pennanen, Teemu & Perkkiö, Ari-Pekka, 2018. "Convex integral functionals of regular processes," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1652-1677.
  11. 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.
  12. 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.
  13. Wang, Rongming & Wang, Zhenpeng, 1997. "Set-Valued Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 180-198, October.
  14. 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.
  15. 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.
  16. 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.
  17. Emmanuel Lepinette & Ilya Molchanov, 2017. "Conditional cores and conditional convex hulls of random sets," Papers 1711.10303, arXiv.org.
  18. 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.
  19. Ilya Molchanov & Anja Muhlemann, 2019. "Nonlinear expectations of random sets," Papers 1903.04901, arXiv.org.
  20. 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.
  21. 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.
  22. Teemu Pennanen, 2011. "Convex Duality in Stochastic Optimization and Mathematical Finance," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 340-362, May.
  23. Henry, Marc, 2007. "A representation of decision by analogy," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 771-794, September.
  24. 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.
  25. Xiaoyou Liu & Xi Fu, 2012. "Control Systems Described by a Class of Fractional Semilinear Evolution Equations and Their Relaxation Property," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
  26. Weixuan Xia, 2023. "Optimal Consumption--Investment Problems under Time-Varying Incomplete Preferences," Papers 2312.00266, arXiv.org, revised Jan 2025.
  27. Bianca Satco, 2024. "A Filippov-Type Lemma for Stieltjes Differential Inclusions with Supremum," Mathematics, MDPI, vol. 12(22), pages 1-13, November.
  28. Johan Jonasson, 1998. "On Positive Random Objects," Journal of Theoretical Probability, Springer, vol. 11(1), pages 81-125, January.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. Bhowmik, Anuj, 2013. "Edgeworth equilibria: separable and non-separable commodity spaces," MPRA Paper 46796, University Library of Munich, Germany.
  34. Lee-Chae Jang, 2011. "On Properties of the Choquet Integral of Interval‐Valued Functions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
  35. 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.
  36. 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.
  37. López-Diaz, Miguel & Gil, Maria Angeles, 1997. "Constructive definitions of fuzzy random variables," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 135-143, December.
  38. 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.
  39. Ilya Molchanov & Anja Mühlemann, 2021. "Nonlinear expectations of random sets," Finance and Stochastics, Springer, vol. 25(1), pages 5-41, January.
  40. De Simone, Anna & Graziano, Maria Gabriella, 2003. "Cone conditions in oligopolistic market models," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 53-73, February.
  41. 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.
  42. 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.
  43. 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.
  44. Weiyin Fei & Yunhe Li & Chen Fei, 2014. "Properties of Solutions to Stochastic Set Differential Equations under Non‐Lipschitzian Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
  45. 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.
  46. 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.
  47. 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.
  48. 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.
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