Nonlinear Dynamics

, Volume 82, Issue 3, pp 1605–1607 | Cite as

Comments on “Solving nonlinear stochastic differential equations with fractional Brownian motion using reducibility approach” [Nonlinear Dyn. 67, 2719–2726 (2012)]

  • Khosro Khandani
  • Vahid Johari Majd
  • Mahdieh Tahmasebi
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Abstract

In this note, some comments are pointed out to the paper (Zeng et al. in Nonlinear Dyn 67:2719–2726, 2012). It is shown that the authors in the mentioned paper have wrongly utilized the fractional Ito formula to derive the reducibility conditions of nonlinear fractional stochastic differential equations (SDEs) to linear fractional SDEs. This incorrect use of the fractional Ito formula has led to fundamental flaws in the proposed theorems.

Keywords

Fractional Ito formula Nonlinear stochastic differential equations Fractional Brownian motion 
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References

  1. 1.
    Zeng, C., Yang, Q., Chen, Y.Q.: Solving nonlinear stochastic differential equations with fractional Brownian motion using reducibility approach. Nonlinear Dyn. 67, 2719–2726 (2012)MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Duncan, T.E., Hu, Y., Pasik-Duncan, B.: Stochastic calculus for fractional Brownian motion. I. Theory. SIAM J. Control Optim. 38, 582–612 (2000)Google Scholar
  3. 3.
    Hu, Y., Zhou, X.Y.: Stochastic control for linear systems driven by fractional noises. SIAM J. Control Optim. 43(6), 2245–2277 (2005)MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Khosro Khandani
    • 1
  • Vahid Johari Majd
    • 1
  • Mahdieh Tahmasebi
    • 2
  1. 1.Intelligent Control Systems Laboratory, School of Electrical and Computer EngineeringTarbiat Modares UniversityTehranIran
  2. 2.School of Mathematics, Department of Applied MathematicsTarbiat Modares UniversityTehranIran

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