Franziska KŘhn

Institut for Mathematical Stochastics


Dr. Franziska KŘhn



Office:Willersbau, Room C235
Zellescher Weg 12 - 14, 01069 Dresden
Phone:    +49-351-463 34276
Fax: +49-351-463 37251
E–Mail: franziska.kuehn1@tu-dresden.de
I am currently on leave as a postdoctoral fellow at the Institute of Mathematics in Toulouse.

E-Mail: franziska.kuhn@math.univ-toulouse.fr

Curriculum vitae

Year of Birth: 1989

Education:

Publications

Books

  • LÚvy-Type Processes: Moments, Construction and Heat Kernel Estimates. Springer Lecture Notes in Mathematics vol. 2187 (vol. VI of the "LÚvy Matters" subseries).
    Springer, 2017. ISBN: 978-3-319-60887-7 • List of misprints

Preprints

  1. Schauder estimates for Poisson equations associated with non-local Feller generators. Submitted.
    Journal • [pdf][arXiv] • DOI
  2. Existence of (Markovian) solutions to martingale problems associated with LÚvy-type operators. Submitted.
    Journal • [pdf][arXiv] • DOI

Papers

  1. Viscosity solutions to Hamilton-Jacobi-Bellman equations associated with sublinear LÚvy(-type) processes.
    ALEA Latin American Journal for Proability and Mathematical Statistics 16 (2019), 531-559.
    Journal[pdf][arXiv] • DOI: 10.30757/ALEA.v16-20
  2. (with RenÚ L. Schilling) A probabilistic proof of Schoenberg's theorem.
    Journal of Mathematical Analysis and Applications 476 (2019), 13-26.
    Journal[pdf][arXiv] • DOI: 10.1016/j.jmaa.2018.11.046
  3. Schauder estimates for equations associated with LÚvy generators.
    Integral Equations and Operator Theory 91:10 (2019).
    Journal[pdf][arXiv] • DOI: 10.1007/s00020-019-2508-4
  4. (with RenÚ L. Schilling) Strong convergence of the Euler-Maruyama approximation for a class of LÚvy-driven SDEs.
    Stochastic Processes and their Applications 129 (2019), 2654-2680.
    Journal[pdf][arXiv] • DOI: 10.1016/j.spa.2018.07.018
  5. Perpetual integrals via random time changes.
    Bernoulli 25 (2019), 1755-1769.
    Journal[pdf] • DOI: 10.3150/18-BEJ1034
    Comment: There is an earlier version of this publication; it is neither a subset nor a superset of the published article:
    Random time changes of Feller processes.
    [pdf][arXiv]
  6. (with RenÚ L. Schilling) On the domain of fractional Laplacians and related generators of Feller processes.
    Journal of Functional Analysis 276 (2019), 2397-2439.
    Journal[pdf][arXiv]Misprints • DOI: 10.1016/j.jfa.2018.12.011
  7. Transition probabilities of LÚvy-type processes: Parametrix construction.
    Mathematische Nachrichten 292 (2019), 358-376.
    Journal [pdf][arXiv] • DOI: 10.1002/mana.201700441
  8. On Martingale Problems and Feller processes.
    Electronic Journal of Probability 23 (2018), 1-18.
    Journal[pdf][arXiv] • DOI: 10.1214/18-EJP142
  9. Solutions of LÚvy-driven SDEs with unbounded coefficients as Feller processes.
    Proceedings of the American Mathematical Society 146 (2018), 3591-3604.
    Journal[pdf][arXiv] • DOI: 10.1090/proc/14022
  10. Existence and estimates of moments for LÚvy-type processes.
    Stochastic Processes and their Applications 127 (2017), 1018-1041.
    [Journal][pdf][arXiv]Misprints • DOI: 10.1016/j.spa.2016.07.008
  11. (with RenÚ L. Schilling) Moderate deviations and Strassen's law for additive processes.
    Journal of Theoretical Probability 29 (2016), 632-652.
    [Journal][pdf][arXiv] • DOI: 10.1007/s10959-014-0584-6

Talks & Presentations

  • Connection between Martingale Problems and Markov processes (Lecture Notes)
    Lecture Series. IRTG Summer School on Probability Theory and Stochastic Dynamics, Bielefeld, Germany, August 19-23, 2019
  • Schauder estimates for non-local operators
    JournÚes de ProbabilitÚs, Dourdan, France, June 24-28, 2019
  • Schauder estimates for non-local operators
    Probability and Analysis 2019, Bedlewo, Poland, May 20-24, 2019
  • Schauder estimates for integro-differential operators
    Seminar "Differential Equations and Dynamical Systems", Wroclaw, Poland, April, 1, 2019
  • Regularity of solutions to Poisson equations associated with LÚvy-type operators
    Seminar "Theory of Markov Semigroups and Schr÷dinger Operators", Wroclaw, Poland, March 29, 2019
  • Kolmogorov equations associated with sublinear Markov processes
    Barcelona-Toulouse Probability Days, Barcelona, Spain, October 4-5, 2018
  • On the domain of fractional Laplacians and related generators of Feller processes
    Joint Meeting UMI-SIMAI-PTM, Wroclaw, Poland, September 17-20, 2018
  • On martingale problems associated with LÚvy-type operators
    JournÚes de ProbabilitÚs, Tours, France, June 25-29, 2018
  • From LÚvy-type Operators to Feller Processes
    Stochastic Processes and their Applications 2018, Gothenburg, Sweden, June 11-15, 2018
  • An Introduction to Feller Processes
    SÚminaire de ProbabilitÚs, Institut de MathÚmatiques de Toulouse, Toulouse, France, January 9, 2018
  • Feller processes and their connection to martingale problems for LÚvy-type operators
    Oberseminar Analysis, Universitńt Bielefeld, Bielefeld, Germany, November 17, 2017
  • On Martingale Problems and Feller Processes
    MaJKo 2017 - Workshop on Jump Processes and Stochastic Analysis, Dresden, Germany, September 1-2, 2017
  • On LÚvy-type processes with unbounded coefficients
    Dresden-Wien Workshop 2017, Dresden, Germany, April 20-22, 2017
  • Transition probabilities for Feller processes: Parametrix construction
    Oberseminar Wahrscheinlichkeitstheorie, Technische Universitńt MŘnchen, MŘnchen, Germany, January 16, 2017
  • Small time asymptotics of generalized moments and applications
    Workshop on 'Dirichlet Forms and Stochastic Analysis', Kansai University, Osaka, Japan, November 12, 2016
  • Feller processes: Parametrix construction
    Poster Session. 8th International Conference on LÚvy Processes, Angers, France, July 24-29, 2016
  • Transition probabilities for Feller processes: Parametrix construction
    MaJKo 2016 - Workshop on Stochastic Analysis and Related Topics, Dresden, Germany, May 9-10, 2016
  • Transition probabilities for Feller processes: Parametrix construction
    German Probability and Statistics Days, Bochum, Germany, March 1-4, 2016
  • Integrated heat kernel estimates and applications
    Swansea, UK, September 30, 2015
  • Existence and estimates of moments for LÚvy-type processes
    Poster Session. German-Japanese conference on Stochastic Analysis and Applications, Tohoku University, Sendai, Japan, August 31 - September 4, 2015
  • Existence and estimates of moments for LÚvy-type processes
    Young Forum, Summer School on Dirichlet Forms and Stochastic Analysis, Kansai University, Osaka, Japan, August 24-28, 2015
  • Moments and heat kernels for SDEs and LÚvy-type processes
    Lecture Series. Erasmus 2015, Swansea, UK, June 1-5, 2015