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A Stability Result for Stochastic Differential Equations Driven by Fractional Brownian Motions

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  • Bruno Saussereau

Abstract

We study the stability of the solutions of stochastic differential equations driven by fractional Brownian motions with Hurst parameter greater than half. We prove that when the initial conditions, the drift, and the diffusion coefficients as well as the fractional Brownian motions converge in a suitable sense, then the sequence of the solutions of the corresponding equations converge in Hölder norm to the solution of a stochastic differential equation. The limit equation is driven by the limit fractional Brownian motion and its coefficients are the limits of the sequence of the coefficients.

Suggested Citation

  • Bruno Saussereau, 2012. "A Stability Result for Stochastic Differential Equations Driven by Fractional Brownian Motions," International Journal of Stochastic Analysis, Hindawi, vol. 2012, pages 1-13, December.
    • Handle: RePEc:hin:jnijsa:281474
    DOI: 10.1155/2012/281474
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    Cited by:

    1. Ioannis Gasteratos & Antoine Jacquier, 2023. "Transportation-cost inequalities for non-linear Gaussian functionals," Papers 2310.05750, arXiv.org.
    2. Xiliang Fan, 2019. "Derivative Formulas and Applications for Degenerate Stochastic Differential Equations with Fractional Noises," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1360-1381, September.

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