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Khasminskii-type theorems for stochastic functional differential equations with infinite delay

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  • Wu, Fuke
  • Hu, Shigeng

Abstract

The classical Khasminskii-type theorem gives a powerful tool to examine the global existence of solutions for stochastic differential equations without the linear growth condition by the use of the Lyapunov functions. However, there is no such result for stochastic functional equations with infinite delay. The main aim of this paper is to establish the existence-and-uniqueness theorems of global solutions for stochastic functional differential equations with infinite delay.

Suggested Citation

  • Wu, Fuke & Hu, Shigeng, 2011. "Khasminskii-type theorems for stochastic functional differential equations with infinite delay," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1690-1694, November.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:11:p:1690-1694
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    References listed on IDEAS

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    1. Mao, Xuerong & Shen, Yi & Yuan, Chenggui, 2008. "Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1385-1406, August.
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    Cited by:

    1. Zhang, Tian & Chen, Huabin, 2019. "The stability with a general decay of stochastic delay differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 294-307.
    2. Mei, Hongwei & Yin, George & Wu, Fuke, 2016. "Properties of stochastic integro-differential equations with infinite delay: Regularity, ergodicity, weak sense Fokker–Planck equations," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3102-3123.
    3. Zhou, Shaobo & Hu, Yangzi, 2016. "Numerical approximation for nonlinear stochastic pantograph equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 126-138.
    4. Fawaz E. Alsaadi & Lichao Feng & Madini O. Alassafi & Reem M. Alotaibi & Adil M. Ahmad & Jinde Cao, 2022. "Stochastic Robustness of Delayed Discrete Noises for Delay Differential Equations," Mathematics, MDPI, vol. 10(5), pages 1-14, February.
    5. Wang, Zhen & Li, Xiong & Lei, Jinzhi, 2014. "Moment boundedness of linear stochastic delay differential equations with distributed delay," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 586-612.
    6. Feng, Lichao & Liu, Lei & Wu, Zhihui & Liu, Qiumei, 2021. "Stability analysis for nonlinear Markov jump neutral stochastic functional differential systems," Applied Mathematics and Computation, Elsevier, vol. 394(C).

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