Research

I investigate non-linear stochastic partial differential equations (SPDEs), especially concerning well-posedness and approximation in time and space. My results include optimal pathwise uniform convergence rates for the temporal approximation of a broad class of hyperbolic SPDEs in 2-smooth Banach spaces. Extending this class further to include more nonlinearities is part of my current work. Moreover, I am always intrigued by applications of C0-semigroup theory and enjoy working at the intersection of stochastic, numerical, and functional analysis. 

I gratefully acknowledge the support of my research by a Feodor Lynen research fellowship awarded by the Alexander von Humboldt foundation.

1. F. Kastner and K. Klioba. Milstein-type schemes for hyperbolic SPDEs. 47 pages. 2025. Preprint on arXiv.

2. K. Klioba and C. Seifert. Approximation of random evolution equations of parabolic type. 39 pages. 2024. Preprint on arXiv, accepted for publication in Journal of Evolution Equations

1. K. Klioba and M. Veraar. Pathwise uniform convergence of time discretization schemes for SPDEs. IMA J. Numer. Anal., 45(4):2060-2131, 2025. Full text here, preprint on arXiv.

2. K. Klioba and M. Veraar. Temporal approximation of stochastic evolution equations with irregular nonlinearities. J. Evol. Eqn., 24(43):1-34, 2024. Full text here, preprint on arXiv.

3. F. Dorfhuber, J. Eisentraut, K. Klioba, J. Křetínský. QuADTool: Attack-Defense-Tree Synthesis, Analysis and Bridge to Verification. QEST+ FORMATS, Lecture Notes in Comput. Sci., 14996:52-71. Springer, 2024. Full text here, preprint on arXiv.

4. J. Eisentraut, S. Holzer, K. Klioba, J. Křetínský, L. Pin, A. Wagner. Assessing security of cryptocurrencies with attack-defense trees: proof of concept and future directions. ICTAC, Lecture Notes in Comput. Sci., 12819:214-234. Springer, 2021. Full text here.

1. K. Klioba. Approximation of evolution equations with random data. Deutsche Nationalbibliothek. PhD thesis, Hamburg University of Technology, 191 pages, 2024. Full text here.

2. K. Klioba and M. Veraar. Stochastic Schroedinger equation. (stochastic-schroedinger-v12). Zenodo. DOI 10.5281/zenodo.12802298. Matlab code pertaining to the 2025 article in IMA J. Numer. Anal., 2024. Available here.

3. E. Frick, D. Dahl, K. Klioba, C. Seifert, M. Lindner, C. Schuster. Quantitative Error Bounds of Polynomial Chaos Expansion and their Application to Resonant Systems. 12 pages, 2019. Preprint here. (based partially on my bachelor thesis)

Last and upcoming conferences:

• upcoming: New horizons in well-posedness of stochastic differential equations, Leiden, the Netherlands, December 2025

• IWOTA 2025: invited talks in sessions 'Operator semigroups and related operators' and 'Linear systems and control theory', Enschede, the Netherlands, July 2025

• Oberwolfach: Workshop 'Stochastic Partial Differential Equations in Critical Spaces', Oberwolfach, Germany, June 2025

• SPDEvent IV: talk on 'Optimal convergence rates in time for hyperbolic SPDEs: A unified approach', Bielefeld, Germany, May 2025

• Analysis and Probability in Infinite Dimensions: poster on 'Semilinear Stochastic Evolution Equations of Hyperbolic type', travel grant by European Women in Mathematics Netherlands, Bad Herrenalb, Germany, April 2025

• Workshop Operator Theory: invited talk on 'Taming uncertainty: Approximation of Random Evolution Equations', Hamburg, Germany, February 2025

Selected awards and prizes:

• 2025-2027: Feodor Lynen Research Fellowship for two-year postdoc at TU Delft awarded by Alexander von Humboldt foundation. 

• 2025-2028: Member of the European Mathematical Society Young Academy (EMYA)

• 2022: Research fellowship for PhD students by German Academic Exchange Service (DAAD) for 6-month stay at TU Delft.

• 2015-2020: Scholarship by the German Academic Scholarship Foundation, Germany's largest, oldest and most prestigious scholarship foundation.  

Please see the CV tab for a complete list of conferences, invited talks, prizes, and awards.