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Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space

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  • Boufoussi, Brahim
  • Hajji, Salah

Abstract

In this note we prove an existence and uniqueness result of mild solutions for a neutral stochastic differential equation with finite delay, driven by a fractional Brownian motion in a Hilbert space and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution.

Suggested Citation

  • Boufoussi, Brahim & Hajji, Salah, 2012. "Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1549-1558.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1549-1558
    DOI: 10.1016/j.spl.2012.04.013
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    References listed on IDEAS

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    1. Nualart, David & Saussereau, Bruno, 2009. "Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 391-409, February.
    2. Nualart, David & Ouknine, Youssef, 2002. "Regularization of differential equations by fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 103-116, November.
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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. Zhi Li & Litan Yan, 2019. "Ergodicity and Stationary Solution for Stochastic Neutral Retarded Partial Differential Equations Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1399-1419, September.
    3. Xu, Liping & Li, Zhi, 2018. "Stochastic fractional evolution equations with fractional brownian motion and infinite delay," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 36-46.
    4. Boufoussi, Brahim & Hajji, Salah, 2017. "Stochastic delay differential equations in a Hilbert space driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 222-229.
    5. Ren, Yong & Hou, Tingting & Sakthivel, R. & Cheng, Xing, 2014. "A note on the second-order non-autonomous neutral stochastic evolution equations with infinite delay under Carathéodory conditions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 658-665.
    6. Nguyen Tien, Dung, 2013. "The existence of a positive solution for a generalized delay logistic equation with multifractional noise," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1240-1246.
    7. Gao, Fengyin & Kang, Yanmei, 2021. "Positive role of fractional Gaussian noise in FitzHugh–Nagumo neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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