Dr. Petru Cioica-Licht

AG Analysis und Angewandte Mathematik - Stochastik

Bild: P. Cioica-Licht
Dr. Petru Cioica-Licht
Telefon
+49 561 804-4587
E-Mail
Standort
Heinrich-Plett-Straße 40
34132 Kassel
Raum
Heinr.-Plett-Str., Raum 1417

Quicklinks  (Dr. Petru Cioica-Licht)

Beruflicher WerdegangForschungPublikationenVerschiedenes

Beruflicher Werdegang  (Dr. Petru Cioica-Licht)

seit 09/2021 Akademischer Rat, Institut für Mathematik, Universität Kassel
01/2019 - 09/2021 Wissenschaftlicher Mitarbeiter, AG Stochastische Analysis, Fakultät für Mathematik, Universität Duisburg-Essen
02/2017 - 07/2018 Lecturer in Mathematics (Assistant Professor), Department of Mathematics and Statistics, University of Otago, Dunedin, Neuseeland
02/2016 - 01/2017 Postdoctoral Fellow im Projekt "Evolution Equations with Memory and Random Fluctuations“, gefördert durch den Marsden Fund der New Zealand Royal Society, University of Otago, Dunedin, Neuseeland
01/2014 - 12/2015 Wissenschaftlicher Mitarbeiter (Postdoc) im DFG-Projekt „Regularitätstheorie stochastischer partieller Differentialgleichungen in (Quasi-)Banachräumen“, Philipps-Universität Marburg
01/2010 - 12/2013 Promotionsstipendiat der Philipps-Universität Marburg

Research  (Dr. Petru Cioica-Licht)

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 Lp-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:

Publikationen  (Dr. Petru Cioica-Licht)

Aufsatz in einer Fachzeitschrift

P. A. Cioica-Licht, S. G. Cox, and M. C. Veraar, “Stochastic integration in quasi-Banach spaces,” Studia Mathematica, vol. 269, no. 1, pp. 1–64, 2023.
http://dx.doi.org/10.4064/sm180424-31-10
P. A. Cioica-Licht, D. Bryant, L. O. Clark, and R. Young, “Inner Products for Convex Bodies,” Journal of Convex Analysis, vol. 28, no. 4, pp. 1249–1264, 2021.
http://dx.doi.org/10.48550/arXiv.1811.03686
P. A. Cioica-Licht and M. Weimar, “On the limit regularity in Sobolev and Besov scales related to approximation theory,” Journal of Fourier Analysis and Applications, vol. 26, pp. 1–26, 2020.
http://dx.doi.org/10.1007/s00041-019-09707-8
P. A. Cioica-Licht, K.-H. Kim, and K. Lee, “On the regularity of the stochastic heat equation on polygonal domains in R2,” Journal of Differential Equations, vol. 267, no. 11, pp. 6447–6479, 2019.
http://dx.doi.org/10.1016/j.jde.2019.06.027
P. A. Cioica-Licht, S. Dahlke, and F. Eckhardt, “Besov regularity for the stationary Navier - Stokes equation on bounded Lipschitz domains,” Applicable Analysis, vol. 97, no. 3, pp. 466–485, 2018.
http://dx.doi.org/10.1080/00036811.2016.1272103
P. A. Cioica-Licht, K.-H. Kim, K. Lee, and F. Lindner, “An Lp-estimate for the stochastic heat equation on an angular domain in R2,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 6, no. 1, pp. 45–72, 2018.
http://dx.doi.org/10.1007/s40072-017-0102-9
P. Cioica, S. Dahlke, N. Döhring, U. Friedrich, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, and R. L. Schilling, “On the Convergence Analysis of the Inexact Linearly Implicit Euler Scheme for a Class of Stochastic Partial Differential Equations,” Potential Analysis, vol. 44, no. 3, pp. 473–495, 2016.
http://dx.doi.org/10.1007/s11118-015-9510-5
P. Cioica, S. Dahlke, N. Döhring, U. Friedrich, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, and R. L. Schilling, “Convergence analysis of spatially adaptive Rothe methods,” Foundations of Computational Mathematics, vol. 14, no. 5, pp. 863–912, 2014.
http://dx.doi.org/10.1007/s10208-013-9183-7
P. Cioica, K.-H. Kim, K. Lee, and F. Lindner, “On the Lq(Lp)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains,” Electronic Journal of Probability, vol. 18, pp. 1–41, 2013.
http://dx.doi.org/10.1214/EJP.v18-2478
P. Cioica, S. Dahlke, N. Döhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, and R. L. Schilling, “Adaptive wavelet methods for the stochastic Poisson equation,” BIT Numerical Mathematics, vol. 52, no. 3, pp. 589–614, 2012.
http://dx.doi.org/10.1007/s10543-011-0368-7
P. Cioica and S. Dahlke, “Spatial Besov regularity for semilinear stochastic partial differential equations on bounded Lipschitz domains,” International Journal of Computer Mathematics, vol. 89, no. 18, pp. 2443–2459, 2012.
http://dx.doi.org/10.1080/00207160.2011.631530
P. Cioica, S. Dahlke, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, and R. L. Schilling, “Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains,” Studia Mathematica, vol. 207, no. 3, pp. 197–234, 2011.
http://dx.doi.org/10.4064/sm207-3-1

Beitrag in einem Sammelband

P. Cioica, S. Dahlke, N. Döhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, and R. L. Schilling, “Adaptive Wavelet Methods for SPDEs,” in Extraction of Quantifiable Information from Complex Systems, vol. 102, S. Dahlke, W. Dahmen, M. Griebel, W. Hackbusch, K. Ritter, R. Schneider, C. Schwab, and H. Yserentant, Eds. Cham: Springer International Publishing, 2014, pp. 83–107.
http://dx.doi.org/10.1007/978-3-319-08159-5_5

Dissertation

P. Cioica, “Besov regularity of stochastic partial differential equations on bounded Lipschitz domains,” Marburg, 2014.
http://dx.doi.org/10.17192/z2014.0223

Preprint

P. A. Cioica-Licht, M. Hutzenthaler, and P. T. Werner, “Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations,” arXiv Preprint. pp. 1–34, 2022.
http://dx.doi.org/10.48550/arXiv.2205.14398
P. A. Cioica-Licht, “An Lp-theory for the stochastic heat equation on angular domains in R2 with mixed weights,” arXiv Preprint. pp. 1–20, 2020.
http://dx.doi.org/10.48550/arXiv.2003.03782

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