Research

My research is mainly concerned with the analysis of the regularity of stochastic partial differential equations (SPDEs) and consequences for their numerical approximation. I am rather driven by specifc questions than by particular techniques. Mathematically, I enjoy in particular the interplay of probability theory and analysis. So far, I have been mainly working on the following topics:

• The development of a comprehensive L_p-theory for SPDEs on non-smooth domains, in particular, on polygons and polyhedra
• The regularity analysis of SPDEs in specific scales of Besov spaces that determine the convergence rate of the best n-term approximation
• The convergence analysis of numerical schemes for (S)PDEs
• The analysis of stochastic Volterra-integral equations

My online research profiles can be found here:

• ORCID
• Google Scholar
• MathSciNet

Here is also a list of my publications (mostly up to date), including links to printable and citable versions:

Preprints

1. An L_p-theory for the stochastic heat equation on angular domains in R² with mixed weights
   2020. arXiv:2003.03782
   [arXiv]

Papers

1. Inner products for Convex Bodies
   (with D.J. Bryant, L. Orloff Clark, R. Young), 2018, 17 pages. To appear in J. Convex Anal.
   [arXiv]

2. On the limit regularity in Sobolev and Besov scales related to approximation theory
   (with M. Weimar)
   J. Fourier Anal. Appl. 26 (1) (2020), Art. 10, 1–24.
   [DOI] [arXiv]

3. On the regularity of the stochastic heat equation on polygonal domains in R²
   (with K.-H. Kim, K. Lee)
   J. Differential Equations 267 (11) (2019) 6447–6479.
   [DOI] [arXiv]

4. Stochastic integration in quasi-Banach spaces
   (with M.C. Veraar, S.G. Cox), 2018, 53 pages. To appear in Studia Math.
   [arXiv]

5. An L_p-estimate for the stochastic heat equation on an angular domain in R²
   (with K.-H. Kim, K. Lee, F. Lindner)
   Stoch. Partial Differ. Equ. Anal. Comput. 6 (1) (2018) 45–72.
   [DOI] [arXiv]

6. Besov regularity for the stationary Navier–Stokes equation on bounded Lipschitz domains
   (with F. Eckhardt, S. Dahlke)
   Appl. Anal. 97 (3) (2018) 466–485.
   [DOI] [arXiv]

7. On the convergence analysis of the inexact linearly implicit Euler scheme for a class of SPDEs
   (with S. Dahlke, N. Döhring, U. Friedrich, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling)
   Potential Anal. 44 (3) (2016) 473–495.
   [DOI] [Preprint] [arXiv]

8. Convergence analysis of spatially adaptive Rothe methods
   (with S. Dahlke, N. Döhring, U. Friedrich, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling)
   Found. Comput. Math. 14 (5) (2014) 863–912.
   [DOI] [Preprint]

9. On the L_q(L_p)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains
   (with K.-H. Kim, K. Lee, F. Lindner)
   Electron. J. Probab. 18 (82) (2013) 1–41.
   [DOI] [Preprint] [arXiv]

10. Spatial Besov regularity for semilinear stochastic partial differential equations on bounded Lipschitz domains
    (with S. Dahlke)
    Int. J. Comput. Math. 89 (18) (2012) 2443–2459.
    [DOI] [Preprint]

11. Adaptive wavelet methods for the stochastic Poisson equation
    (with S. Dahlke, N. Döhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling)
    BIT 52 (3) (2012) 589–614.
    [DOI] [Preprint]

12. Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains
    (with S. Dahlke, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling)
    Studia Math. 207 (3) (2011) 197–234.
    [DOI] [Preprint] [arXiv]

Book chapters (refereed)

1. Adaptive wavelet methods for SPDEs
   (with with S. Dahlke, N. Döhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling)
   In: Extraction of Quantifiable Information from Complex Systems
   (S. Dahlke, W. Dahmen, M. Griebel, W. Hackbusch, K. Ritter, R. Schneider, C. Schwab, H. Yserentant, eds.)
   Lecture Notes in Computational Science and Engineering, vol. 102, Springer, 2014, pp. 83-107.
   [DOI] [Book]

Reports

1. Regularity of stochastic partial differential equations in Besov spaces related to adaptive schemes
   Oberwolfach Report No. 2/2015, pp. 20-22.
   [DOI]

PhD Thesis

Besov Regularity of Stochastic Partial Differential Equations on Bounded Lipschitz Domains
Referees: Prof. Dr. Stephan Dahlke (Marburg) • Prof. Dr. René L. Schilling (Dresden) • Prof. Dr. Stig Larsson (Chalmers, Göteborg)
Defended on 17 February 2014 at Philipps-Universität Marburg (summa cum laude).
Published by Logos Verlag Berlin, 2015. ISBN: 987-3-8325-3920-7
[pdf] [Printed]

Diplomarbeit (Master thesis)

Konvergenzraten von Raum-Zeit-Approximationen stochastischer Evolutionsgleichungen
(Rates of Convergence of Space Time Approximations for Stochastic Evolution Equations)
Advisors: Prof. Dr. Stephan Dahlke (Marburg) and Prof. Dr. René L. Schilling (Dresden)
[pdf]