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Stochastic Differential Inclusions

In: Stochastic Differential Inclusions and Applications

Author

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  • Michał Kisielewicz

    (University of Zielona Góra)

Abstract

This chapter is devoted to the theory of stochastic differential inclusions. The main results deal with stochastic functional inclusions defined by set-valued functional stochastic integrals. Subsequent sections discuss properties of stochastic and backward stochastic differential inclusions.

Suggested Citation

  • Michał Kisielewicz, 2013. "Stochastic Differential Inclusions," Springer Optimization and Its Applications, in: Stochastic Differential Inclusions and Applications, edition 127, chapter 0, pages 147-179, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-6756-4_4
    DOI: 10.1007/978-1-4614-6756-4_4
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    Citations

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    Cited by:

    1. Miguel de Carvalho & Gabriel Martos, 2022. "Modeling interval trendlines: Symbolic singular spectrum analysis for interval time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(1), pages 167-180, January.
    2. Zachary Feinstein & Birgit Rudloff, 2015. "A Supermartingale Relation for Multivariate Risk Measures," Papers 1510.05561, arXiv.org, revised Jan 2018.
    3. Weixuan Xia, 2023. "Set-valued stochastic integrals for convoluted L\'{e}vy processes," Papers 2312.01730, arXiv.org, revised Nov 2024.
    4. Beatrice Acciaio & Anastasis Kratsios & Gudmund Pammer, 2022. "Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer," Papers 2201.13094, arXiv.org, revised Mar 2023.
    5. Ahmed, Hamdy M. & Zhu, Quanxin, 2023. "Exploration nonlocal controllability for Hilfer fractional differential inclusions with Clarke subdifferential and nonlinear noise," Statistics & Probability Letters, Elsevier, vol. 195(C).
    6. Jessada Tariboon & Sotiris K. Ntouyas & Bashir Ahmad & Ahmed Alsaedi, 2020. "Existence Results for Sequential Riemann–Liouville and Caputo Fractional Differential Inclusions with Generalized Fractional Integral Conditions," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    7. Bashir Ahmad & Ahmed Alsaedi & Sotiris K. Ntouyas & Hamed H. Al-Sulami, 2019. "On Neutral Functional Differential Inclusions involving Hadamard Fractional Derivatives," Mathematics, MDPI, vol. 7(11), pages 1-13, November.
    8. Ahmed Alsaedi & Ravi P. Agarwal & Sotiris K. Ntouyas & Bashir Ahmad, 2020. "Fractional-Order Integro-Differential Multivalued Problems with Fixed and Nonlocal Anti-Periodic Boundary Conditions," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    9. 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.
    10. Çağın Ararat & Zachary Feinstein, 2021. "Set-valued risk measures as backward stochastic difference inclusions and equations," Finance and Stochastics, Springer, vol. 25(1), pages 43-76, January.
    11. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2021. "A note on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1003-1026.
    12. Sotiris K. Ntouyas & Bashir Ahmad & Jessada Tariboon, 2022. "( k , ψ )-Hilfer Nonlocal Integro-Multi-Point Boundary Value Problems for Fractional Differential Equations and Inclusions," Mathematics, MDPI, vol. 10(15), pages 1-20, July.

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