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) as well as on topics related to fractional Brownian motion.
See also the individual profil pages of each researcher.
Publications of the Chair in the last 5 years
- 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.
- Neuenkirch, A. and Shalaiko, T. (2016). The maximum rate of convergence for the approximation of the fractional Lévy area at a single point. Journal of Complexity, 33, 107-117.
- Akhtari, B., Babolian, E. and Neuenkirch, A. (2015). An Euler scheme for stochastic delay differential equations on unbounded domains: pathwise convergence. Discrete and Continuous Dynamical Systems : DCDS, Series B, 20, 23-38.
- Altmayer, M. and Neuenkirch, A. (2015). Multilevel Monte Carlo Quadrature of Discontinuous Payoffs in the Generalized Heston Model using Malliavin Integration by Parts. SIAM Journal on Financial Mathematics : SIFIN, 6, 22-52.
- Neuenkirch, A. and Shalaiko, T. (2015). The relation between mixed and rough SDEs and its application to numerical methods. Stochastic Analysis and Applications, 33, 927-942.
- Neuenkirch, A. and Szpruch, L. (2014). First order strong approximations of scalar SDEs defined in a domain. Numerische Mathematik, 128, 103-136.
- Parczewski, P. (2014). A Wick functional limit theorem. Probability and Mathematical Statistics, 34, 127-145.
- Parczewski, P. (2014). A fractional Donsker theorem. Stochastic Analysis and Applications, 32, 328-347.
- Altmayer, M. (2015). Quadrature of discontinuous SDE functionals using Malliavin integration by parts. München: Verlag Dr. Hut.
- Altmayer, M., Dereich, S., Li, S., Müller-Gronbach, T., Neuenkirch, A., Ritter, K. and Yaroslavtseva, L. (2014). Constructive quantization and multilevel algorithms for quadrature of stochastic differential equations. In Dahlke, S. Extraction of Quantifiable Information from Complex Systems (S. 109-132). Cham: Springer International Publishing.
- Koch, S. (2019). Sensitivity results in stochastic analysis. Dissertation, . Mannheim.
- Altmayer, M. (2015). Quadrature of discontinuous SDE functionals using Malliavin integration by parts. Dissertation, . Mannheim.