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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. repec:eee:apmaco:v:305:y:2017:i:c:p:299-307 is not listed on IDEAS
    2. 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.
    3. repec:eee:stapro:v:129:y:2017:i:c:p:222-229 is not listed on IDEAS

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