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Infinite-delayed stochastic impulsive differential systems with Poisson jumps

Author

Listed:
  • Surendra Kumar

    (University of Delhi)

  • Shobha Yadav

    (University of Delhi)

Abstract

This manuscript investigates a broad class of stochastic differential equation steered by Poisson jumps and impulses in a Hilbert space. We use successive approximation method to show the existence of a solution. The continuous dependence of the solutions to the initial data is also studied. Finally, the existence of optimal state-control pair for the associated Lagrangian problem is discussed. An example is also presented to validate the theoretical results.

Suggested Citation

  • Surendra Kumar & Shobha Yadav, 2021. "Infinite-delayed stochastic impulsive differential systems with Poisson jumps," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 344-362, June.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:2:d:10.1007_s13226-021-00123-7
    DOI: 10.1007/s13226-021-00123-7
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    References listed on IDEAS

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    1. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," The Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
    2. Y. Ren & Q. Zhou & L. Chen, 2011. "Existence, Uniqueness and Stability of Mild Solutions for Time-Dependent Stochastic Evolution Equations with Poisson Jumps and Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 315-331, May.
    3. Luo, Jiaowan & Liu, Kai, 2008. "Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 864-895, May.
    4. P. Balasubramaniam & P. Tamilalagan, 2017. "The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 139-155, July.
    5. JinRong Wang & Yong Zhou & Milan Medveď, 2012. "On the Solvability and Optimal Controls of Fractional Integrodifferential Evolution Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 31-50, January.
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    Cited by:

    1. Kuang, Daipeng & Li, Jianli & Gao, Dongdong & Luo, Danfeng, 2024. "Stochastic near-optimal control for a system with Markovian switching and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Upadhyay, Anjali & Kumar, Surendra, 2023. "The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke’s subdifferential," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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