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

  • Raphael Zimmer (PhD student)
  • Mateusz Majka (PhD student)

Recent Preprints

  • A.Eberle, A.Guillin, R.Zimmer: Couplings and quantitative contraction rates for Langevin dynamics (Preprint March 2017), arXiv:1703.01617
  • A.Eberle, R.Zimmer: Sticky couplings of multidimensional diffusions with different drifts (Preprint December 2016), arXiv:1612.06125
  • A.Eberle, A.Guillin, R.Zimmer: Quantitative Harris type theorems for diffusions and McKean-Vlasov processes (Preprint June 2016), arXiv:1606.06012
Reflection couplings and contraction rates for diffusions (Revised Preprint June 2014, 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, Preprint July 2011, final version published in PTRF 155, 2013)PDF
Reflection coupling and Wasserstein contractivity without convexity
(Preprint August 2011, final version published in C.R. Math. Acad. Sci. Paris 349, 2011)
PDF
Stability of nonlinear flows of probability measures related to sequential MCMC methods (with Carlo Marinelli, working paper May 2011)PDF

 

Previous PhD students

  • Nikolaus Schweizer (Non-asymptotic error bounds for sequential MCMC methods, PhD 2011, currently Universität Duisburg-Essen)
  • Daniel Gruhlke (Transition path sampling and Multi-Level MCMC methods, PhD 2014)