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Asymptotic stability of nonlinear impulsive stochastic differential equations

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  • Sakthivel, R.
  • Luo, J.

Abstract

In this paper, we study the existence and asymptotic stability in p-th moment of mild solutions of nonlinear impulsive stochastic differential equations. A fixed point approach is employed for achieving the required result.

Suggested Citation

  • Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:9:p:1219-1223
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    References listed on IDEAS

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    1. Liu, Kai & Mao, Xuerong, 1998. "Exponential stability of non-linear stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 173-193, November.
    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. Ignatyev, Oleksiy, 2009. "Partial asymptotic stability in probability of stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 597-601, March.
    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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    Cited by:

    1. Tamilalagan, P. & Balasubramaniam, P., 2017. "Moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 299-307.
    2. Alka Chadha & Dwijendra N. Pandey, 2018. "Approximate Controllability of a Neutral Stochastic Fractional Integro-Differential Inclusion with Nonlocal Conditions," Journal of Theoretical Probability, Springer, vol. 31(2), pages 705-740, June.
    3. Peng, Shiguo & Jia, Baoguo, 2010. "Some criteria on pth moment stability of impulsive stochastic functional differential equations," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1085-1092, July.
    4. Cheng, Pei & Deng, Feiqi, 2010. "Global exponential stability of impulsive stochastic functional differential systems," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1854-1862, December.
    5. Kao, Yonggui & Zhu, Quanxin & Qi, Wenhai, 2015. "Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 795-804.
    6. Yao, Fengqi & Deng, Feiqi, 2012. "Exponential stability in terms of two measures of impulsive stochastic functional differential systems via comparison principle," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1151-1159.
    7. Long, Shujun & Teng, Lingying & Xu, Daoyi, 2012. "Global attracting set and stability of stochastic neutral partial functional differential equations with impulses," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1699-1709.
    8. Singh, Ajeet & Shukla, Anurag & Vijayakumar, V. & Udhayakumar, R., 2021. "Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    9. Chen, Guiling & van Gaans, Onno & Lunel, Sjoerd Verduyn, 2018. "Existence and exponential stability of a class of impulsive neutral stochastic partial differential equations with delays and Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 7-18.

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