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Stochastic functional differential equations of Sobolev-type with infinite delay

Author

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  • Revathi, P.
  • Sakthivel, R.
  • Ren, Yong

Abstract

Stochastic differential equations have been widely used to model a number of phenomena in diverse fields of science and engineering. In this paper, we focus on the local existence of mild solution for a class of stochastic functional differential equations of Sobolev-type with infinite delay. Furthermore, the results are extended to study the local existence results for neutral stochastic differential equations of Sobolev-type. Using the semigroup theory and fixed point argument, we establish a set of sufficient conditions for obtaining the required result. Furthermore, existence results for integro-differential equations of Sobolev-type is also discussed. Finally, an example is provided to illustrate the obtained theory.

Suggested Citation

  • Revathi, P. & Sakthivel, R. & Ren, Yong, 2016. "Stochastic functional differential equations of Sobolev-type with infinite delay," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 68-77.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:68-77
    DOI: 10.1016/j.spl.2015.10.019
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    References listed on IDEAS

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    1. Michal Fec̆kan & JinRong Wang & Yong Zhou, 2013. "Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 79-95, January.
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    Cited by:

    1. Yao-Qun Wu & Jia Wei He, 2022. "Existence and Optimal Controls for Hilfer Fractional Sobolev-Type Stochastic Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 79-101, October.
    2. Yong-Kui Chang & Yatian Pei & Rodrigo Ponce, 2019. "Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 558-572, August.

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