Stochastic differential equations
Strong and weak approximation, non-globally Lipschitz dynamics and robust time-stepping methods.
Research group · Institute of Mathematics
Numerics of Stochastic Differential Equations
We develop and analyse reliable numerical methods for stochastic differential equations, stochastic evolution equations and uncertainty-aware computation.
Research
Research
Our work combines stochastic analysis with numerical analysis. We are particularly interested in methods whose stability, convergence and computational cost can be understood rigorously.
Stochastic evolution equations
Space-time discretisation of stochastic partial differential equations and regularity of their solutions.
Randomised numerical methods
Monte Carlo methods, randomised quadrature and algorithms for time-irregular problems.
News
News
Cornelia Rips joins the group
Cornelia Rips has joined our research group as a doctoral researcher.
New preprint on a randomized SDIRK method
A new preprint analyses the error and stability of a randomized singly diagonally implicit Runge-Kutta method.
Appointment as Vice-Dean for Education (2022–2026)
Raphael Kruse served as Vice-Dean for Education in the Faculty of Natural Sciences II from September 2022 to August 2026.
People
People
Researchers and colleagues behind our work. Every profile opens to contact details, research information and related publications.
Raphael Kruse
Professor · Head of the groupProf. Dr Raphael Kruse works on numerical methods and stochastic analysis for stochastic differential and evolution equations, as well as Monte Carlo methods.
Open profile
Cornelia Rips
Doctoral researcherCornelia Rips is a doctoral researcher. Her research interests include the analysis and numerical approximation of conservation laws.
Open profile
Maren Hantke
Lecturer and researcherPD Dr Maren Hantke studies the analysis and numerical solution of hyperbolic differential equations, including models from fluid dynamics.
Open profile
Anett Schröder
SecretaryAnett Schröder is the secretary for the research groups in Applied Analysis, Functional Analysis, Numerical Mathematics and Numerics of Stochastic Differential Equations.
Open profile
Publication
Selected publications
2026
Preprint
Error Bound and Stability Analysis for a Randomized Singly Diagonally Implicit Runge-Kutta Method
arXiv preprint arXiv:2607.18928
2026
Journal article
Application of randomized quadrature formulas to the finite element method for elliptic equations
BIT Numerical Mathematics, vol. 66, no. 2, article 31
2023
Journal article
The BDF2-Maruyama method for the stochastic Allen–Cahn equation with multiplicative noise
Journal of Computational and Applied Mathematics, vol. 419, article 114634
2019
Journal article
A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients
Discrete & Continuous Dynamical Systems - Ser. B, vol. 24(8), 3475-3502
Contact
Visit and contact us
Enter the Georg-Cantor-Haus and take the stairs to the first floor. Our offices are at the end of the long corridor.
Address
Institute of MathematicsMartin Luther University Halle-Wittenberg
Theodor-Lieser-Str. 5
06120 Halle (Saale)
Germany