Dr. Claudine von Hallern

Research Interest

My research focus is the numerical analysis of stochastic differential equations, particularly, stochastic partial differential equations (SPDEs). I develop and analyze numerical methods for this class of equations and I am especially concerned with higher order schemes that are free of derivatives.

Moreover, I am motivated by particular applications - Uncertainty is an important factor in the ocean sciences. Therefore, I investigate the impact of uncertainties in ocean models and work on numerical schemes for the specific SPDEs that are involved.

Publications

• Claudine von Hallern and Andreas Rößler, A Derivative-Free Milstein Type Approximation Method
  for SPDEs covering the Non-Commutative Noise case, ArXiv e-prints, arXiv:2006.08275, 2020,
  submitted
• Claudine von Hallern and Andreas Rößler: An Analysis of the Milstein Scheme for SPDEs
  without a Commutative Noise Condition. In: Tuffin B., L’Ecuyer P. (eds) Monte Carlo and Quasi-
  Monte Carlo Methods. MCQMC 2018. Springer Proceedings in Mathematics & Statistics, vol
  324. Springer, Cham, 2020.
  doi: 10.1007/978-3-030-43465-6_25
• Claudine Leonhard and Andreas Rößler, Iterated Stochastic Integrals in Infinite Dimensions:
  Approximation and Error Estimates. 2019, Stoch PDE: Anal Comp., 7(2), 209–239.
  doi: 10.1007/s40072-018-0126-9.
• Volkmar Sauerland, Ulrike Löptien, Claudine Leonhard, Andreas Oschlies, and Anand Srivas-
  tav, Error assessment of biogeochemical models by lower bound methods. 2018, Geosci.
  Model Dev., 11, 1181-1198.
  doi: 10.5194/gmd-11-1181-2018
• Claudine Leonhard and Andreas Rößler, Enhacing the order of the Milstein scheme for SPDEs
  with commutative noise. 2018, SIAM J. Numer. Anal., 56(4), 2585–2622.
  doi: 10.1137/16M1094087
• Britta Kubera, Claudine Leonhard, Andreas Rößler, Achim Peters, Stress-related changes in
  body shape – Results from the Whitehall II study. 2017, Obesity, 25: 1625–1632.
  doi: 10.1002/oby.21928