Mathematics
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Department of Mathematics & Statistics
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Dr Petru Cioica-Licht

Office: Science III, room 212
Phone: 479 7783
Email: pcioica@maths.otago.ac.nz


I left to Duisburg-Essen, Germany (Postdoc with Prof. Dr. Martin Hutzenthaler, Start: January 2019).

Contact: I keep using my Otago email address.

Homepage: I keep updating this webpage.


Welcome to my webpage @Otago U!

Scroll down to find out more about

  • my research interests
  • my publications
  • my teaching
  • my collaborators

and some other infos!

News

Research Interests

Stochastic Partial Differential Equations (SPDEs).

In particular,

  • Regularity of SPDEs in scales of Besov spaces related to non-linear approximation;
  • Lp-theory for SPDEs on non-smooth domains;
  • Regularity of SPDEs with memory/Stochastic Volterra Integral Equations;
  • Numerical methods for SPDEs.

Publications

Papers

  1. An $L_p$-estimate for the stochastic heat equation on an angular domain in $\mathbb R^2$
    (with K.-H. Kim, K. Lee, F. Lindner) Stoch. Partial Differ. Equ. Anal. Comput. 6 (1) (2018) 45--72.
    (arXiv) (DOI: 10.1007/s40072-017-0102-9)
  2. Besov regularity for the stationary Navier–Stokes equation on bounded Lipschitz domains
    (with F. Eckhardt, S. Dahlke) Appl. Anal. 97 (3) (2018) 466-485.
    (arXiv) (DOI: 10.1080/00036811.2016.1272103)
  3. 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.
    (arXiv) (DOI: 10.1007/s11118-015-9510-5)
  4. 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.
    (Preprint) (DOI: 10.1007/s10208-013-9183-7)
  5. On the Lq(Lp)-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.
    (arXiv) (DOI: 10.1214/EJP.v18-2478)
  6. 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.
    (Preprint) (DOI: 10.1080/00207160.2011.631530)
  7. 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.
    (Preprint) (DOI: 10.1007/s10543-011-0368-7)
  8. 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.
    (arXiv) (DOI: 10.4064/sm207-3-1)

Preprints

  1. On the regularity of the stochastic heat equation on polygonal domains in $\mathbb R^2$
    (with K.-H. Kim and K. Lee), 2018, 28 pages.
    (arXiv)
  2. Stochastic integration in quasi-Banach spaces
    (with Mark C. Veraar and Sonja G. Cox), 2018, 53 pages.
    (arXiv)

Book chapters (refereed)

  1. Adaptive wavelet methods for SPDEs
    (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.
    (chapter) (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: 10.4171/OWR/2015/2)

PhD thesis

  1. Besov Regularity of Stochastic Partial Differential Equations on Bounded Lipschitz Domains
    defended on 17 February 2014 @ Philipps-Universität Marburg (summa cum laude)
    Published by Logos Verlag Berlin, 2015.
    (thesis) (ISBN: 987-3-8325-3920-7)

Master thesis (Diplomarbeit; in German)

  1. Konvergenzraten von Raum-Zeit-Approximationen stochastischer Evolutionsgleichungen
    (Rates of Convergence of Space Time Approximations for Stochastic Evolution Equations).
    (thesis)

Teaching

@Otago U

  • 2018, Semester 1: MATH4MI Measure and Integration
  • 2018, Semester 1: MATH301 Hilbert spaces
  • 2017, Semester 2: MATH160/102 Calculus (Second Half)
  • 2017, Semester 1: MATH4MI Measure and Integration
  • 2017, Semester 1: MATH4PT Probability Theory
  • 2016, Semester 2: MATH4FA Functional Analysis
  • 2016, Semester 1: MATH4MI Measure and Integration

@Philipps-Universität Marburg

Supervised theses

  • Frank Eckhardt, Besov-Regularität elliptischer Randwertprobleme (Besov Regularity of Elliptic Boundary Value Problems), Master thesis. Jointly supervised with Stephan Dahlke @Philipps-Universität Marburg
  • Eugenia Heiner, Stochastische Evolutionsgleichungen in Banachräumen (Stochastic Evolution Equations in Banach Spaces), Master thesis. Jointly supervised with Stephan Dahlke @Philipps-Universität Marburg

Collaborators

I work/worked together with (active/inactive in alphabetical order):

Miscellaneous

Reviewer

Scholarships

Prizes

  • PhD Prize of the Philipps-Universität Marburg (2014)