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The existence and exponential stability for neutral stochastic partial differential equations with infinite delay and poisson jump

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  • Huabin Chen

    (Nanchang University, Nanchang)

Abstract

In this paper, the problems on the existence and uniqueness, the exponential stability in mean square for mild solution of neutral stochastic partial differential equations with infinite delay and Poisson jump are considered. Firstly, the existence and uniqueness for mild solution of such systems is studied by using the Banach fixed point theorem. Then, by establishing an integral inequality, the exponential stability in mean square for mild solution to neutral stochastic partial differential equations with infinite delay and Poisson jump is discussed. Compared with the previous works, our method is new and our results can generalize and improve some existing results. Finally, an example is given to show the effectiveness of the obtained results.

Suggested Citation

  • Huabin Chen, 2015. "The existence and exponential stability for neutral stochastic partial differential equations with infinite delay and poisson jump," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(2), pages 197-217, April.
    • Handle: RePEc:spr:indpam:v:46:y:2015:i:2:d:10.1007_s13226-015-0113-z
    DOI: 10.1007/s13226-015-0113-z
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    References listed on IDEAS

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    1. Chen, Huabin, 2010. "Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 50-56, January.
    2. Liu, Kai & Truman, Aubrey, 2000. "A note on almost sure exponential stability for stochastic partial functional differential equations," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 273-278, November.
    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. Wan, Li & Duan, Jinqiao, 2008. "Exponential stability of non-autonomous stochastic partial differential equations with finite memory," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 490-498, April.
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