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h-stability for stochastic Volterra–Levin equations

Author

Listed:
  • Li, Zhi
  • Long, Qinyi
  • Xu, Liping
  • Wen, Xueqi

Abstract

In this paper, we investigate a class of stochastic Volterra–Levin equation. By using fixed point theory, some sufficient conditions ensuring the considered equations are h-stable in the mean square and almost surely are obtained. Some known results are improved and generalized. In the end, two examples are given to illustrate the feasibility and effectiveness of results obtained.

Suggested Citation

  • Li, Zhi & Long, Qinyi & Xu, Liping & Wen, Xueqi, 2022. "h-stability for stochastic Volterra–Levin equations," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008773
    DOI: 10.1016/j.chaos.2022.112698
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    References listed on IDEAS

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    1. Li, Zhi & Zhang, Wei, 2017. "Stability in distribution of stochastic Volterra–Levin equations," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 20-27.
    2. Caraballo, Tomás & Belfeki, Mohsen & Mchiri, Lassaad & Rhaima, Mohamed, 2021. "h-stability in pth moment of neutral pantograph stochastic differential equations with Markovian switching driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. 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.
    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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