Open Access
Issue
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
Page(s) 1981 - 2006
DOI https://doi.org/10.1051/m2an/2023015
Published online 03 July 2023
  1. X. Dai and A. Xiao, Lévy-driven stochastic Volterra integral equations with doubly singular kernels: existence, uniqueness, and a fast EM method. Adv. Comput. Math. 46 (2020) 29. [CrossRef] [Google Scholar]
  2. X. Dai and A. Xiao, A note on Euler method for the overdamped generalized Langevin equation with fractional noise. Appl. Math. Lett. 111 (2021) 106669. [CrossRef] [Google Scholar]
  3. R.C. Dalang, Extending the martingale measure stochastic integral with applications to spatially homogeneous S.P.D.E’.s. Electron. J. Probab. 4 (1999) 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  4. G. Didier and H. Nguyen, Asymptotic analysis of the mean squared displacement under fractional memory kernels. SIAM J. Math. Anal. 52 (2020) 3818–3842. [CrossRef] [MathSciNet] [Google Scholar]
  5. D. Fang and L. Li, Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise. ESAIM Math. Model. Numer. Anal. 54 (2020) 431–463. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  6. M.B. Giles, Multilevel Monte Carlo path simulation. Oper. Res. 56 (2008) 607–617. [CrossRef] [MathSciNet] [Google Scholar]
  7. M.B. Giles, Multilevel Monte Carlo methods. Acta Numer. 24 (2015) 259–328. [CrossRef] [MathSciNet] [Google Scholar]
  8. D.J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43 (2001) 525–546. [NASA ADS] [CrossRef] [Google Scholar]
  9. D.J. Higham, X. Mao and A.M. Stuart, Strong convergence of Euler-type methods for nonlinear stochastic differential equations. SIAM J. Numer. Anal. 40 (2002) 1041–1063. [CrossRef] [MathSciNet] [Google Scholar]
  10. J. Hong, C. Huang, M. Kamrani and X. Wang, Optimal strong convergence rate of a backward Euler type scheme for the Cox–Ingersoll–Ross model driven by fractional Brownian motion. Stochastic Process. Appl. 130 (2020) 2675–2692. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Hutzenthaler, A. Jentzen and P.E. Kloeden, Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 467 (2011) 1563–1576. [MathSciNet] [Google Scholar]
  12. S. Jiang, J. Zhang, Q. Zhang and Z. Zhang, Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations. Commun. Comput. Phys. 21 (2017) 650–678. [Google Scholar]
  13. P.E. Kloeden, A. Neuenkirch and R. Pavani, Multilevel Monte Carlo for stochastic differential equations with additive fractional noise. Ann. Oper. Res. 189 (2011) 255–276. [CrossRef] [MathSciNet] [Google Scholar]
  14. S.C. Kou, Stochastic modeling in nanoscale biophysics: subdiffusion within proteins. Ann. Appl. Stat. 2 (2008) 501–535. [MathSciNet] [Google Scholar]
  15. S.C. Kou and X. Sunney Xie, Generalized Langevin equation with fractional Gaussian noise: subdiffusion within a single protein molecule. Phys. Rev. Lett. 93 (2004) 180603. [CrossRef] [PubMed] [Google Scholar]
  16. R. Kubo, The fluctuation–dissipation theorem. Rep. Prog. Phys. 29 (1966) 255–284. [CrossRef] [Google Scholar]
  17. L. Li and J.-G. Liu, A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows. SIAM J. Numer. Anal. 57 (2019) 2095–2120. [CrossRef] [MathSciNet] [Google Scholar]
  18. L. Li, J.-G. Liu and J. Lu, Fractional stochastic differential equations satisfying fluctuation-dissipation theorem. J. Stat. Phys. 169 (2017) 316–339. [Google Scholar]
  19. X. Mao, Stochastic Differential Equations and Applications, 2nd edition. Horwood Publishing Limited, Chichester (2008). [Google Scholar]
  20. S.A. McKinley and H.D. Nguyen, Anomalous diffusion and the generalized Langevin equation. SIAM J. Math. Anal. 50 (2018) 5119–5160. [CrossRef] [MathSciNet] [Google Scholar]
  21. H. Mori, Transport, collective motion, and Brownian motion. Progr. Theoret. Phys. 33 (1965) 423–455. [CrossRef] [Google Scholar]
  22. D. Nualart, The Malliavin Calculus and Related Topics, 2nd edition. Springer-Verlag, Berlin (2006). [Google Scholar]
  23. V. Pipiras and M.S. Taqqu, Integration questions related to fractional Brownian motion. Probab. Theory Relat. Fields 118 (2000) 251–291. [CrossRef] [Google Scholar]
  24. A. Richard, X. Tan and F. Yang, Discrete-time simulation of stochastic Volterra equations. Stochastic Process. Appl. 141 (2021) 109–138. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. Sanz-Solé, Malliavin Calculus with Applications to Stochastic Partial Differential Equations. EPFL Press, distributed by CRC Press (2005). [CrossRef] [Google Scholar]
  26. H. Ye, J. Gao and Y. Ding, A generalized Gronwall inequality and its application to a fractional differential equation. J. Math. Anal. Appl. 328 (2007) 1075–1081. [Google Scholar]

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