Open Access
Issue |
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
|
|
---|---|---|
Page(s) | 1153 - 1184 | |
DOI | https://doi.org/10.1051/m2an/2024031 | |
Published online | 27 June 2024 |
- 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]
- 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]
- 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]
- 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]
- 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]
- M. Chak, Regularity preservation in Kolmogorov equations for non-Lipschitz coefficients under Lyapunov conditions. Preprint arXiv:2209.05436 (2022). [Google Scholar]
- 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]
- A. Debussche and E. Faou, Weak backward error analysis for SDEs. SIAM J. Numer. Anal. 50 (2012) 1735–1752. [Google Scholar]
- 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]
- 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]
- M. Hairer, M. Hutzenthaler and A. Jentzen, Loss of regularity for Kolmogorov equations. Ann. Probab. 43 (2015) 468–527. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- L. Journel and P. Monmarché, Convergence of the kinetic annealing for general potentials. Electron. J. Probab. 27 (2022) 1–37. [CrossRef] [Google Scholar]
- M. Kopec, Weak backward error analysis for Langevin process. BIT 55 (2015) 1057–1103. [CrossRef] [MathSciNet] [Google Scholar]
- M. Kopec, Weak backward error analysis for overdamped Langevin processes. IMA J. Numer. Anal. 35 (2015) 583–614. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- T. Lelièvre and G. Stoltz, Partial differential equations and stochastic methods in molecular dynamics. Acta Numer. 25 (2016) 681–880. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Lu and J.-C. Mattingly, Geometric ergodicity of Langevin dynamics with Coulomb interactions. Nonlinearity 33 (2020) 675–699. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- P. Monmarché, Generalized Γ calculus and application to interacting particles on a graph. Potential Anal. 50 (2019) 439–466. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- G. Stoltz and Z. Trstanova, Langevin dynamics with general kinetic energies. Multiscale Model. Simul. 16 (2018) 777–806. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- 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]
- M.E. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation. Oxford University Press (2023). [Google Scholar]
- C. Villani, Hypocoercivity. Mem. Amer. Math. Soc. 202 (2009) iv+141. [Google Scholar]
- K. Yosida, Functional Analysis, reprint of the 6th edition. Springer-Verlag, Berlin (1994). [Google Scholar]
- C. Zhang, Hypocoercivity and global hypoellipticity for the kinetic Fokker-Planck equation in Hk spaces. Preprint arXiv:2012.06253 (2020). [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.