Math @ Duke

Publications [#339404] of Jianfeng Lu
Papers Published
 Li, L; Liu, JG; Lu, J, Fractional stochastic differential equations satisfying fluctuationdissipation theorem
(April, 2017)
(last updated on 2019/02/21)
Abstract: We consider in this work stochastic differential equation (SDE) model for particles in contact with a heat bath when the memory effects are nonnegligible. As a result of the fluctuationdissipation theorem, the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives and based on this we consider fractional stochastic differential equations (FSDEs), which should be understood in an integral form. We establish the existence of strong solutions for such equations. In the linear forcing regime, we compute the solutions explicitly and analyze the asymptotic behavior, through which we verify that satisfying fluctuationdissipation indeed leads to the correct physical behavior. We further discuss possible extensions to nonlinear forcing regime, while leave the rigorous analysis for future works.


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