Photo credit: Anna Logue
Research
Currently, we focus on questions arising in
- stochastic numerics,
- information based complexity,
- stochastic analysis,
in particular, on numerical methods for stochastic differential equations (non-standard assumptions, quadrature problems and lower error bounds).
See also the individual profil pages of each researcher.
Publications of the Chair in the last 5 years
- Mickel, A. and Neuenkirch, A. (2023). The weak convergence order of two Euler-type discretization schemes for the log-Heston model. IMA Journal of Numerical Analysis : IMAJNA (forthcoming).
- Mickel, A. and Neuenkirch, A. (2021). The weak convergence rate of two semi-exact discretization schemes for the Heston model. Risks : Open Access Journal, 9, Article 23.
- Neuenkirch, A. and Szölgyenyi, M. (2020). The Euler-Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem. IMA Journal of Numerical Analysis : IMAJNA, 1–28.
- Göttlich, S., Lux, K. and Neuenkirch, A. (2019). The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate. Advances in Difference Equations : ADE, 2019, 1–21.
- Koch, S. and Neuenkirch, A. (2019). The Mandelbrot-van Ness fractional Brownian motion is infinitely differentiable with respect to its Hurst parameter. Discrete and Continuous Dynamical Systems : DCDS. Series B, 24, 3865–3880.
- Neuenkirch, A., Szölgyenyi, M. and Szpruch, L. (2019). An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis. SIAM Journal on Numerical Analysis, 57, 378–403.
- Bender, C. and Parczewski, P. (2018). Discretizing Malliavin calculus. Stochastic Processes and Their Applications, 128, 2489 – 2537.
- Duc, L. H., Garrido-Atienza, M. J., Neuenkirch, A. and Schmalfuß, B. (2018). Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in (1/2,1). Journal of Differential Equations, 264, 1119–1145.
- Garrido-Atienza, M. J., Neuenkirch, A. and Schmalfuß, B. (2018). Asymptotical stability of differential equations driven by Hölder continuous paths. Journal of Dynamics and Differential Equations, 30, 359–377.
- Koch, S. (2018). Directional Malliavin derivatives: A characterisation of independence and a generalised chain rule. Communications on Stochastic Analysis, 12, 137–156.
- Neuenkirch, A. and Parczewski, P. (2018). Optimal approximation of skorohod integrals. Journal of Theoretical Probability, 31, 206–231.
- Altmayer, M. and Neuenkirch, A. (2017). Discretising the Heston model: an analysis of the weak convergence rate. IMA Journal of Numerical Analysis : IMAJNA, 37, 1930–1960.
- Parczewski, P. (2017). Donsker-type theorems for correlated geometric fractional Brownian motions and related processes. Electronic Communications in Probability : ECP, 22, 1–13.
- Parczewski, P. (2017). Extensions of the Hitsuda–Skorokhod integral. Communications on Stochastic Analysis, 11, 479–490.
- Parczewski, P. (2017). Optimal approximation of Skorohod integrals – examples with substandard rates. Communications on Stochastic Analysis, 11, 43–61.
- Parczewski, P. (2017). The self-normalized Donsker theorem revisited. Modern Stochastics: Theory and Applications, 4, 189–198.
- Koch, S. (2019). Sensitivity results in stochastic analysis. Dissertation, . Mannheim.
- Neuenkirch, A. (2021). D. Higham, P. Kloeden: “An introduction to the numerical simulation of stochastic differential equations”. Review, Jahresbericht der Deutschen Mathematiker-Vereinigung