Dr. Petru Cioica-Licht
AG Analysis und Angewandte Mathematik - Stochastik
Bild: Privat
- Telefon
- +49 561 804-4587
- cioica-licht[at]mathematik.uni-kassel[dot]de
- Standort
- Heinrich-Plett-Straße 40
34132 Kassel
- Raum
- Heinr.-Plett-Str., Raum 1417
Beruflicher Werdegang
| 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
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:
Here is also a list of my publications (mostly up to date), including links to printable and citable versions:
Publikationen
Aufsatz in einer Fachzeitschrift
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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 |
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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/https://doi.org/10.48550/arXiv.1811.03686 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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
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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. |
Preprint
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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.” pp. 1–34, 2022. http://dx.doi.org/10.48550/arXiv.2205.14398 |
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P. A. Cioica-Licht, “An Lp-theory for the stochastic heat equation on angular domains in R2 with mixed weights.” pp. 1–20, 2020. http://dx.doi.org/10.48550/arXiv.2003.03782 |
Projekte
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2018 Regularity of Stochastic Partial Differential Equations on Non-Smooth Domains https://forschung.uni-kassel.de/converis/portal/detail/Project/130258717 15.07.2018 |
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2016 Evolution Equations with Memory and Random Fluctuations https://forschung.uni-kassel.de/converis/portal/detail/Project/130259125 15.01.2017 |
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2015 NRF-DAAD Bilateral Scientist Exchange Program https://forschung.uni-kassel.de/converis/portal/detail/Project/130258845 15.07.2015 |
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2014 Regularitätstheorie stochastischer partieller Differentialgleichungen in (Quasi-)Banachräumen https://forschung.uni-kassel.de/converis/portal/detail/Project/130258957 15.12.2015 |