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Research topics and surveys

Research group

  • Nawaf Bou-Rabee (Visiting Professor)
  • Katharina Schuh (PhD student)

Previous PhD students

  • Nikolaus Schweizer (Non-asymptotic error bounds for sequential MCMC methods, PhD 2011, currently Tilburg University)
  • Daniel Gruhlke (Transition path sampling and Multi-Level MCMC methods, PhD 2014)
  • Raphael Zimmer (Couplings and Kantorovich contractions with explicit rates for diffusions, PhD 2017)
  • Mateusz B. Majka (Stability of stochastic differential equations with jumps by the coupling method, PhD 2017, currently University of Warwick)

Recent Preprints

  • N.Bou-Rabee, A.Eberle: Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions (Preprint), arXiv:1909.07962
  • A.Durmus, A.Eberle, A.Guillin, R.Zimmer: An elementary approach to uniform in time propagation of chaos (to appear in Proceedings AMS), arXiv:1805.11387
  • N.Bou-Rabee, A.Eberle, R.Zimmer: Coupling and convergence for Hamiltonian Monte Carlo (to appear in Annals of Applied Probability), arXiv:1805.00452

Selected publications

  • A.Eberle, R.Zimmer: Sticky couplings of multidimensional diffusions with different drifts (published in Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, 2019, Vol. 55, No. 4, 2370–2394), (pdf)
  • A.Eberle, A.Guillin, R.Zimmer: Couplings and quantitative contraction rates for Langevin dynamics (published in Annals of Probability, Volume 47, Nr. 4, 2019) (pdf)
  • A.Eberle, M.B.Majka: Quantitative contraction rates for Markov chains on general state spaces (published in Electronic Journal of Probability, Volume 24, 2019) (pdf)
  • A.Eberle, A.Guillin, R.Zimmer: Quantitative Harris type theorems for diffusions and McKean-Vlasov processes (final version published in Transactions AMS, Volume 371, Nr. 10, 2019)  arXiv:1606.06012
  • A. Eberle: Reflection couplings and contraction rates for diffusions (final version published in PTRF 166, December 2016, is available at Springer via http://dx.doi.org/10.1007/s00440-015-0673-1)
  • A. Eberle: Error bounds for Metropolis-Hastings algorithms applied to perturbations of Gaussian measures in high dimensions (Published in at http://dx.doi.org/10.1214/13-AAP926 the Annals of Applied Probability http://www.imstat.org/aap/ 2014)
  • A. Eberle, C. Marinelli: Quantitative approximations of evolving probability measures and sequential MCMC methods (final version published in PTRF 155, 2013)
  • A. Eberle: Reflection coupling and Wasserstein contractivity without convexity
    (final version published in C.R. Math. Acad. Sci. Paris 349, 2011)