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:

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

### Preprints

**An L**_{p}-theory for the stochastic heat equation on angular domains in R^{2}with mixed weights

2020. arXiv:2003.03782

**[arXiv]**

### Papers

**Inner products for Convex Bodies**

(with D.J. Bryant, L. Orloff Clark, R. Young), 2018, 17 pages. To appear in*J. Convex Anal.*

**[arXiv]****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]****On the regularity of the stochastic heat equation on polygonal domains in R**^{2}

(with K.-H. Kim, K. Lee)*J. Differential Equations***267**(11) (2019) 6447–6479.**[DOI]****[arXiv]****Stochastic integration in quasi-Banach spaces**

(with M.C. Veraar, S.G. Cox), 2018, 53 pages. To appear in*Studia Math.*

**[arXiv]****An L**_{p}-estimate for the stochastic heat equation on an angular domain in R^{2}

(with K.-H. Kim, K. Lee, F. Lindner)*Stoch. Partial Differ. Equ. Anal. Comput.***6**(1) (2018) 45–72.**[DOI]****[arXiv]****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]****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]****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]****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]****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]****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]****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)

**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

**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]**