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Stability in distribution of stochastic Volterra–Levin equations

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  • Li, Zhi
  • Zhang, Wei

Abstract

In this paper, we are concerned with a class of stochastic Volterra–Levin equations. By the weak convergence approach, we have a try to deal with the stability conditions in distribution of the segment process of the solutions to the stochastic systems under investigation. Last, an example is presented to illustrate our theory in the work.

Suggested Citation

  • Li, Zhi & Zhang, Wei, 2017. "Stability in distribution of stochastic Volterra–Levin equations," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 20-27.
    • Handle: RePEc:eee:stapro:v:122:y:2017:i:c:p:20-27
    DOI: 10.1016/j.spl.2016.10.022
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    References listed on IDEAS

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    1. 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.
    2. Reiß, M. & Riedle, M. & van Gaans, O., 2006. "Delay differential equations driven by Lévy processes: Stationarity and Feller properties," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1409-1432, October.
    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.
    4. Gushchin, Alexander A. & Küchler, Uwe, 2000. "On stationary solutions of delay differential equations driven by a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 195-211, August.
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    Cited by:

    1. Li, Zhi & Long, Qinyi & Xu, Liping & Wen, Xueqi, 2022. "h-stability for stochastic Volterra–Levin equations," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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