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Stability in distribution of neutral stochastic functional differential equations

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  • Tan, Li
  • Jin, Wei
  • Suo, Yongqiang

Abstract

In this note, by the weak convergence approach, we investigate stability in distribution for a range of neutral stochastic functional differential equations. As a byproduct, our result derived also implies existence of invariant measure of the semigroup generated by the segment process. Last but not least, we close some gaps of Lemma 2, and improve greatly Lemma 4 due to Hu and Wang (2012).

Suggested Citation

  • Tan, Li & Jin, Wei & Suo, Yongqiang, 2015. "Stability in distribution of neutral stochastic functional differential equations," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 27-36.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:27-36
    DOI: 10.1016/j.spl.2015.07.033
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    References listed on IDEAS

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    1. Tan, Li & Jin, Wei & Hou, Zhenting, 2013. "Weak convergence of functional stochastic differential equations with variable delays," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2592-2599.
    2. Yuan, Chenggui & Mao, Xuerong, 2003. "Asymptotic stability in distribution of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 277-291, February.
    3. Bao, Jianhai & Hou, Zhenting & Yuan, Chenggui, 2009. "Stability in distribution of neutral stochastic differential delay equations with Markovian switching," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1663-1673, August.
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    Cited by:

    1. Asker Hussein K., 2020. "Well-Posedness and Exponential Estimates for the Solutions to Neutral Stochastic Functional Differential Equations with Infinite Delay," Journal of Systems Science and Information, De Gruyter, vol. 8(5), pages 434-446, October.

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