Open Access
Volume 58, Number 3, May-June 2024
Page(s) 1153 - 1184
Published online 27 June 2024
  1. L. Angeli, D. Cristan and M. Ottobre, Uniform in time convergence of numerical schemes for stochastic differential equations via Strong Exponential stability: Euler methods, Split-Step and Tamed Schemes. Preprint arXiv:2303.15463 (2023). [Google Scholar]
  2. D. Bakry, I. Gentil and M. Ledoux, Analysis and Geometry of Markov Diffusion Operators. Vol. 348 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Cham (2014). [CrossRef] [Google Scholar]
  3. F. Baudoin, M. Gordina and D.-P. Herzog, Gamma calculus beyond Villani and explicit convergence estimates for Langevin dynamics with singular potentials. Arch. Ration. Mech. Anal. 241 (2021) 765–804. [CrossRef] [MathSciNet] [Google Scholar]
  4. E. Camrud, D.-P. Herzog, G. Stoltz and M. Gordina, Weighted L2-contractivity of Langevin dynamics with singular potentials. Nonlinearity 35 (2022) 998–1035. [CrossRef] [MathSciNet] [Google Scholar]
  5. E. Cancès, F. Legoll and G. Stoltz, Theoretical and numerical comparison of some sampling methods for molecular dynamics. ESAIM: M2AN 41 (2007) 351–389. [CrossRef] [EDP Sciences] [Google Scholar]
  6. M. Chak, Regularity preservation in Kolmogorov equations for non-Lipschitz coefficients under Lyapunov conditions. Preprint arXiv:2209.05436 (2022). [Google Scholar]
  7. F. Conrad and M. Grothaus, Construction, ergodicity and rate of convergence of N-particle Langevin dynamics with singular potentials. J. Evol. Equ. 10 (2010) 623–662. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. Debussche and E. Faou, Weak backward error analysis for SDEs. SIAM J. Numer. Anal. 50 (2012) 1735–1752. [Google Scholar]
  9. A. Durmus, A. Guillin and P. Monmarché, Geometric ergodicity of the bouncy particle sampler. Ann. Appl. Probab. 30 (2020) 2069–2098. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Grothaus and P. Stilgenbauer, A hypocoercivity related ergodicity method for singularly distorted non-symmetric diffusions. Integr. Equ. Oper. Theory 83 (2015) 331–379. [CrossRef] [Google Scholar]
  11. M. Hairer, M. Hutzenthaler and A. Jentzen, Loss of regularity for Kolmogorov equations. Ann. Probab. 43 (2015) 468–527. [CrossRef] [MathSciNet] [Google Scholar]
  12. D.-P. Herzog and J.-C. Mattingly, Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials. Comm. Pure Appl. Math. 72 (2019) 2231–2255. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Hutzenthaler and A. Jentzen, On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients. Ann. Probab. 48 (2020) 53–93. [CrossRef] [MathSciNet] [Google Scholar]
  14. 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]
  15. M. Hutzenthaler, A. Jentzen and P.-E. Kloeden, Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Ann. Appl. Probab. 22 (2012) 1611–1641. [MathSciNet] [Google Scholar]
  16. M. Hutzenthaler, A. Jentzen and X. Wang, Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations. Math. Comput. 87 (2018) 1353–1413. [Google Scholar]
  17. L. Journel and P. Monmarché, Convergence of the kinetic annealing for general potentials. Electron. J. Probab. 27 (2022) 1–37. [CrossRef] [Google Scholar]
  18. M. Kopec, Weak backward error analysis for Langevin process. BIT 55 (2015) 1057–1103. [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Kopec, Weak backward error analysis for overdamped Langevin processes. IMA J. Numer. Anal. 35 (2015) 583–614. [CrossRef] [MathSciNet] [Google Scholar]
  20. B. Leimkuhler, C. Matthews and G. Stoltz, The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics. IMA J. Numer. Anal. 36 (2016) 13–79. [Google Scholar]
  21. T. Lelièvre and G. Stoltz, Partial differential equations and stochastic methods in molecular dynamics. Acta Numer. 25 (2016) 681–880. [CrossRef] [MathSciNet] [Google Scholar]
  22. Y. Lu and J.-C. Mattingly, Geometric ergodicity of Langevin dynamics with Coulomb interactions. Nonlinearity 33 (2020) 675–699. [CrossRef] [MathSciNet] [Google Scholar]
  23. J.-C. Mattingly, A.-M. Stuart and D.-J. Higham, Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise. Stochastic Process. Appl. 101 (2002) 185–232. [CrossRef] [MathSciNet] [Google Scholar]
  24. P. Monmarché, Generalized Γ calculus and application to interacting particles on a graph. Potential Anal. 50 (2019) 439–466. [CrossRef] [MathSciNet] [Google Scholar]
  25. P. Monmarché, High-dimensional MCMC with a standard splitting scheme for the underdamped Langevin diffusion. Electron. J. Stat. 15 (2021) 4117–4166. [MathSciNet] [Google Scholar]
  26. G. Stoltz and Z. Trstanova, Langevin dynamics with general kinetic energies. Multiscale Model. Simul. 16 (2018) 777–806. [CrossRef] [MathSciNet] [Google Scholar]
  27. D. Talay, Stochastic Hamiltonian systems: exponential convergence to the invariant measure, and discretization by the implicit Euler scheme. Markov Process. Related Fields 8 (2002) 163–198. [MathSciNet] [Google Scholar]
  28. D. Talay and L. Tubaro, Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Anal. Appl. 8 (1990) 483–509. [CrossRef] [MathSciNet] [Google Scholar]
  29. M.E. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation. Oxford University Press (2023). [Google Scholar]
  30. C. Villani, Hypocoercivity. Mem. Amer. Math. Soc. 202 (2009) iv+141. [Google Scholar]
  31. K. Yosida, Functional Analysis, reprint of the 6th edition. Springer-Verlag, Berlin (1994). [Google Scholar]
  32. C. Zhang, Hypocoercivity and global hypoellipticity for the kinetic Fokker-Planck equation in Hk spaces. Preprint arXiv:2012.06253 (2020). [Google Scholar]

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