Publications

Books

• Lévy-Type Processes: Moments, Construction and Heat Kernel Estimates.
  Springer Lecture Notes in Mathematics vol. 2187 (vol. VI of the "Lévy Matters" subseries).
  Springer, 2017. ISBN: 978-3-319-60887-7 • List of misprints
• (with  René L. Schilling)
  Counterexamples in Measure and Integration.
  Cambridge University Press, 2021. ISBN: 9781009001625 • Homepage of this book

Paper

• [22] (with  René L. Schilling) Maximal Inequalities and Some Applications. 
  Probability Surveys 20 (2023) 382-485
  Journal • pdf • arXiv • DOI: 10.1214/23-PS17
• [21] (with Markus Kunze) Feller generators with measurable lower order terms. 
  Positivity 26 (2022), article number 85
  Journal  • pdf  • arXiv  • DOI: 10.1007/s11117-022-00948-4
• [20] (with David Berger and René L. Schilling): Lévy processes, generalized moments and uniform integrability. 
  Probability and Mathematical Statistics 42 (2022), 109-131. 
  Journal  • pdf  • arXiv • DOI: 10.37190/0208-4147.00045
• [19]  Upper functions for Lévy(-type) processes. 
  Bernoulli 28 (2022), 2874-2908.
  Journal • pdf • arXiv • DOI: 10.3150/21-BEJ1441
• [18] Interior Schauder estimates for elliptic equations associated with Lévy operators. Potential Analysis 56 (2022), 459–481
  Journal • [pdf] • [arXiv] • DOI: 10.1007/s11118-020-09892-y
• [17] (with  René L. Schilling) Convolution inequalities for Besov and Triebel-Lizorkin spaces, and applications to convolution semigroups.
  Studia Mathematica 262 (2022), 93-119
  Journal • pdf • arXiv • DOI: 10.4064/sm210127-23-3
• [16] (with René L. Schilling)  For which functions are f(X_t)-Ef(X_t) and g(X_t)/Eg(X_t) martingales?
  Theory of Probability and Mathematical Statistics 105 (2021). 79-91
  Journal • pdf • arXiv • DOI: 10.1090/tpms/1157
• [15] Schauder estimates for Poisson equations associated with non-local Feller generators.
  Journal of Theoretical Probability 34 (2021), 1506-1578.
  Journal • [pdf] • [arXiv] • DOI: 10.1007/s10959-020-01008-x
• [14] On infinitesimal generators of sublinear Markov semigroups.
  Osaka Journal of Mathematics 58 (2021), 487-508.
  Journal • [pdf] • [arXiv] • DOI
• [13] A Liouville theorem for Lévy generators.
  Positivity 25 (2021), 997-1012
  Journal • [pdf] • [arXiv] • DOI: 10.1007/s11117-020-00800-7
• [12] Existence of (Markovian) solutions to martingale problems associated with Lévy-type operators.
  Electronic Journal of Probability 25 (2020), 1-26.
  Journal • [pdf] • [arXiv] • DOI: 10.1214/20-EJP424
• [11] Viscosity solutions to Hamilton-Jacobi-Bellman equations associated with sublinear Lévy(-type) processes.
  ALEA Latin American Journal for Proability and Mathematical Statistics 16 (2019), 531-559.
  Journal • [pdf] • [arXiv] • DOI: 10.30757/ALEA.v16-20
• [10] (with René 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
•  [9] Schauder estimates for equations associated with Lévy generators.
  Integral Equations and Operator Theory 91:10 (2019).
  Journal • [pdf] • [arXiv] • DOI: 10.1007/s00020-019-2508-4
• [8] (with René L. Schilling) Strong convergence of the Euler-Maruyama approximation for a class of Lévy-driven SDEs.
  Stochastic Processes and their Applications 129 (2019), 2654-2680.
  Journal • [pdf] • [arXiv] • Correction • DOI: 10.1016/j.spa.2018.07.018 
• [7] 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 René 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
• [5] Transition probabilities of Lévy-type processes: Parametrix construction.
  Mathematische Nachrichten 292 (2019), 358-376.
  Journal • [pdf] • [arXiv] • DOI: 10.1002/mana.201700441
• [4] On Martingale Problems and Feller processes.
  Electronic Journal of Probability 23 (2018), 1-18.
  Journal • [pdf] • [arXiv] • DOI: 10.1214/18-EJP142
• [3] Solutions of Lévy-driven SDEs with unbounded coefficients as Feller processes.
  Proceedings of the American Mathematical Society 146 (2018), 3591-3604.
  Journal • [pdf] • [arXiv] • Misprints • DOI: 10.1090/proc/14022
• [2] Existence and estimates of moments for Lévy-type processes.
  Stochastic Processes and their Applications 127 (2017), 1018-1041.
  [Journal] • [pdf] • [arXiv] • Misprints • DOI: 10.1016/j.spa.2016.07.008
• [1] (with René 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