Probability and Stochastic Analysis - University of Bonn
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Research topics and surveys

Couplings, contractivity and quantitative convergence bounds for diffusionsPDF PDF
Metropolis-Hastings algorithms in high dimensionsPDF PDF
Monte Carlo methods for sequences of probability measuresPDF
Analysis on path and loop spacesPDF PDF
Uniqueness problems for diffusion semigroupsPDF

Research group

  • Katharina Schuh (PhD student)

Recent Preprints

  • A.Eberle, M.B.Majka: Quantitative contraction rates for Markov chains on general state spaces (Preprint August 2018), arXiv:1808.07033
  • A.Durmus, A.Eberle, A.Guillin, R.Zimmer: An elementary approach to uniform in time propagation of chaos (Preprint May 2018), arXiv:1805.11387
  • N.Bou-Rabee, A.Eberle, R.Zimmer:Coupling and convergence for Hamiltonian Monte Carlo (Preprint May 2018), arXiv:1805.00452
  • A.Eberle, A.Guillin, R.Zimmer: Couplings and quantitative contraction rates for Langevin dynamics (to appear in Annals of Probability), arXiv:1703.01617
  • A.Eberle, R.Zimmer: Sticky couplings of multidimensional diffusions with different drifts (to appear in Annales IHP (B), Prob. et Stat.), arXiv:1612.06125
  • A.Eberle, A.Guillin, R.Zimmer: Quantitative Harris type theorems for diffusions and McKean-Vlasov processes (to appear in Transactions AMS), arXiv:1606.06012
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)PDF
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)PDF
Quantitative approximations of evolving probability measures and sequential MCMC methods (with Carlo Marinelli: final version published in PTRF 155, 2013)PDF
Reflection coupling and Wasserstein contractivity without convexity
(final version published in C.R. Math. Acad. Sci. Paris 349, 2011)
PDF

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 King's College London)