Re­se­arch in­te­rests

  • Analysis and numerics of stochastic (partial) differential equations
  • Stochastic differential-algebraic equations, stochastic fiber dynamics
  • Jump processes, Lévy noise
  • Uncertainty quantification
  • Applications of probability theory and statistics in science and engineering

Cur­rent PhD stu­dents


Pu­bli­ca­ti­ons and Pre­prints

Preprints:

  • A. Andersson, F. Lindner: Malliavin regularity and weak approximation of semilinear SPDE with Lévy noise. [arXiv] 22 pages, 2018.
  • F. Lindner, H. Stroot: Strong convergence of a half-explicit Euler scheme for constrained stochastic mechanical systems. [arXiv] 39 pages, 2017. 
  • A. Andersson, F. Lindner: Poisson Malliavin calculus in Hilbert space with an application to SPDE. [arXiv] 48 pages, 2017. 
  • M. Kovács, F. Lindner: Weak error analysis via functional Itô calculus. [arXiv] 33 pages, 2016.

Journal papers:

  • P.A. Cioica-Licht, K.-H. Kim, K. Lee, F. Lindner: An Lp estimate for the stochastic heat equation on an angular domain in R^2. Stoch PDE: Anal Comp 6(1), 45-72, 2018.
  • F. Lindner, N. Marheineke, H. Stroot, A. Vibe, R. Wegener: Stochastic fiber dynamics in a spatially semi-discrete setting. Stoch. Dyn.17(2), 1750016, 29 pages, 2017.
  • P.A. Cioica, S. Dahlke, N. Döhring, U. Friedrich, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling: On the convergence analysis of the inexact linearly implicit Euler scheme for a class of SPDEs. Potential Analysis44(3), 473-495, 2016.
  • M. Kovács, F. Lindner, R.L. Schilling: Weak convergence of finite element approximations of linear stochastic evolution equations with additive Lévy noise. SIAM/ASA Journal on Uncertainty Quantification3(1), 1159-1199, 2015.
  • F. Lindner: Singular Behavior of the Solution to the Stochastic Heat Equation on a Polygonal Domain. Stoch PDE: Anal Comp2(2), 146-195, 2014.
  • P.A. Cioica, S. Dahlke, N. Döhring, U. Friedrich, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling: Convergence Analysis of Spatially Adaptive Rothe Methods. Found Comput Math.14(5), 863-912, 2014.
  • F. Lindner, R.L. Schilling: Weak Order for the Discretization of the Stochastic Heat Equation Driven by Impulsive Noise. Potential Analysis38(2), 345-379, 2013.
  • P.A. Cioica, K.-H. Kim, K. Lee, F. Lindner: On the Lq(Lp)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains. Electronic Journal of Probability18(82), 1-41, 2013.
  • P.A. Cioica, S. Dahlke, N. Döhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling: Adaptive Wavelet Methods for the Stochastic Poisson Equation. BIT. Numerical Mathematics52(3), 589-614. 2012.
  • P.A. Cioica, S. Dahlke, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling: Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains. Studia Mathematica207(3), 197-234, 2011.

Conference proceeding:

  • F. Lindner, H. Stroot, R. Wegener: Semi-discretized stochastic fiber dynamics: Non-linear drag force. (to appear in the Proceedings of ECMI 2016, 7 pages)

Book chapter:

  • P.A. Cioica, S. Dahlke, N. Döhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling: Adaptive Wavelet Methods for SPDEs. 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 102, 83-107, 2014.

Thesis:

  • F. Lindner: Approximation and Regularity of Stochastic PDEs. TU Dresden. Shaker-Verlag, Aachen, 2011.

Teaching

  • Summer semester 2018
    • Lecture: Wahrscheinlichkeitstheorie (Teil 2)
    • Lecture: Maß- und Integrationstheorie
    • Lecture: Biometrie (Einführung in die Statistik)
    • Seminar: Fachseminar Stochastik & Analysis für L3/L4-Master 
  • Winter semester 2017/18
    • Lecture: Wahrscheinlichkeitstheorie (Teil 1)
    • Lecture: Stochastik für Ingenieure (Höhere Mathematik IV)
    • Lecture: Elementare Stochastik

At TU Kaiserslautern:

  • Summer semester 2017
    • Lecture: Introduction to stochastic partial differential equations
    • Lecture: Maß- und Integrationstheorie
  • Winter semester 2016/17
    • Lecture: Stochastic differential equations
    • Lecture: Einführung in die Funktionalanalysis
  • Summer semester 2016
    • Lecture: Statistik II für Wirtschaftswissenschaftler
    • Seminar: Rough paths and regularity structures
    • Proseminar: Endliche Markovketten
  • Winter semester 2015/16
    • Lecture: Stochastische Methoden
  • Summer semester 2015
    • Lecture: Monte Carlo-Algorithmen
    • Seminar: Rough paths and regularity structures
  • Winter semester 2014/15
    • Lecture: Probability theory
  • Summer semester 2014
    • Lecture: Malliavin calculus and applications
  • Winter semester 2013/14
    • Lecture: Introduction to stochastic partial differential equations

At TU Dresden:

  • Summer semester 2013
    • Lecture: Stochastic processes