A note on Euler method for the overdamped generalized Langevin equation with fractional noise

DOI10.1016/j.aml.2020.106669zbMath1450.65002OpenAlexW3048194140MaRDI QIDQ2006358

Ai-Guo Xiao, Xinjie Dai

Publication date: 8 October 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2020.106669

zbMATH Keywords

fractional Brownian motionconvergence rateEuler methodweakly singular kernelgeneralized Langevin equation

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Numerical methods for integral equations (65R20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Numerical solutions to stochastic differential and integral equations (65C30) Fractional partial differential equations (35R11)

Related Items (6)

Exponential stability and synchronisation of fuzzy Mittag–Leffler discrete-time Cohen–Grossberg neural networks with time delays ⋮ An explicit method for the self-interacting diffusion driven by fractional Brownian motion under global Lipschitz conditions ⋮ Strong error analysis of Euler methods for overdamped generalized Langevin equations with fractional noise: Nonlinear case ⋮ The overdamped generalized Langevin equation with Hermite noise ⋮ Strong \(1.5\) order scheme for fractional Langevin equation based on spectral approximation of white noise ⋮ Strong convergence rate of the Euler scheme for SDEs driven by additive rough fractional noises

Cites Work

• Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
• Fluid-particle dynamics for passive tracers advected by a thermally fluctuating viscoelastic medium
• Lévy-driven stochastic Volterra integral equations with doubly singular kernels: existence, uniqueness, and a fast EM method
• Analytic approaches of the anomalous diffusion: a review
• Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion
• Numerics for the fractional Langevin equation driven by the fractional Brownian motion
• Well-posedness and EM approximations for non-Lipschitz stochastic fractional integro-differential equations
• Anomalous Diffusion and the Generalized Langevin Equation
• Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise

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