Foto: 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

Artikel
Bücher
Dissertationen

Neuenkirch, A. und 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, tba, 1-28.
Göttlich, S., Lux, K. und 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. und 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. und 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. und Parczewski, P. (2018). Discretizing Malliavin calculus. Stochastic Processes and Their Applications, 128, 2489 - 2537.
Duc, L. H., Garrido-Atienza, M. J., Neuenkirch, A. und 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. und 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. und Parczewski, P. (2018). Optimal approximation of skorohod integrals. Journal of Theoretical Probability, 31, 206-231.
Altmayer, M. und 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. und 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. und 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. und 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. und Shalaiko, T. (2015). The relation between mixed and rough SDEs and its application to numerical methods. Stochastic Analysis and Applications, 33, 927-942.

Altmayer, M. (2015). Quadrature of discontinuous SDE functionals using Malliavin integration by parts. München: Verlag Dr. Hut.

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.

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