Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

@inproceedings{Li2017FractionalSD,
  title={Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem},
  author={Lei Li and Jian-Guo Liu and Jianfeng Lu},
  year={2017}
}
Wepropose in this work a fractional stochastic differential equation (FSDE)model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the ‘fluctuation-dissipation theorem’, the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the… CONTINUE READING

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