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Existence, Uniqueness and Stability of Mild Solutions for Time-Dependent Stochastic Evolution Equations with Poisson Jumps and Infinite Delay

Author

Listed:
  • Y. Ren

    (Anhui Normal University)

  • Q. Zhou

    (Beijing University of Posts and Telecommunications)

  • L. Chen

    (Anhui Normal University)

Abstract

In this paper, we study a class of time-dependent stochastic evolution equations with Poisson jumps and infinite delay. We establish the existence, uniqueness and stability of mild solutions for these equations under non-Lipschitz condition with Lipschitz condition being considered as a special case. An application to the stochastic nonlinear wave equation, with Poisson jumps and infinite delay, is given to illustrate the obtained theory.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:2:d:10.1007_s10957-010-9792-0
    DOI: 10.1007/s10957-010-9792-0
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    References listed on IDEAS

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    1. Albeverio, S. & Mandrekar, V. & Rüdiger, B., 2009. "Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 835-863, March.
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    Cited by:

    1. 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.

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