Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

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Sensitivity Analysis of Nonlocal Operators with Applications to Jump Processes

2018/31/G/ST1/02252

Keywords:

Lévy(-type) process non-local operator parametrix method global properties of jump processes statistics of stochastic processes approximation of jump processes

Descriptors:

  • ST1_13:
  • ST1_11:

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Politechnika Wrocławska

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Krzysztof Michał Bogdan 

Number of co-investigators in the project: 4

Call: BEETHOVEN 3 - announced on 2018-09-14

Amount awarded: 599 151 PLN

Project start date (Y-m-d): 2020-01-15

Project end date (Y-m-d): 2024-01-14

Project duration:: 48 months (the same as in the proposal)

Project status: Project settled

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Information in the final report

  • Publication in academic press/journals (25)
  1. An extension of the Liouville theorem for Fourier multipliers to sub-exponentially growing solutions
    Authors:
    David Berger, René Schilling, Eugene Shargorodsky, Teo Sharia
    Academic press:
    Journal of Spectral Theory (rok: 2024, tom: 14, strony: 665-695), Wydawca: European Mathematical Society Publishing House
    Status:
    Published
    DOI:
    10.4171/JST/509 - link to the publication
  2. For which functions are $f(X_t)-Ef(X_t)$ and $g(X_t)/E g(X_t)$ martingales?
    Authors:
    Franziska Kühn, René Schilling
    Academic press:
    Theory of Probability and Mathematical Statistics (rok: 2021, tom: 105, strony: 79-91), Wydawca: AMS
    Status:
    Published
    DOI:
    10.1090/tpms/1157 - link to the publication
  3. Approximation of the invariant measure of stable SDEs by an Euler-Maruyama scheme
    Authors:
    Peng Chen, Changsong Deng, René Schilling, Lihu Xu
    Academic press:
    Stochastic Processes and Their Applications (rok: 2023, tom: 163, strony: 136-167), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2023.06.001 - link to the publication
  4. Maximal inequalities and applications
    Authors:
    Franziska Kühn, René Schilling
    Academic press:
    Probability Surveys (rok: 2023, tom: 20, strony: 382-485), Wydawca: Institute of Mathematical Statistics
    Status:
    Published
    DOI:
    10.1214/23-PS17 - link to the publication
  5. Convolution inequalities for Besov and Triebel-Lizorkin spaces, and applications to convolution semigroups
    Authors:
    Franziska Kühn, René Schilling
    Academic press:
    Studia Mathematica (rok: 2022, tom: 262, strony: 93-119), Wydawca: IM PAN
    Status:
    Published
    DOI:
    10.4064/sm210127-23-3 - link to the publication
  6. Maximum likelihood estimation for discrete exponential families and random graphs
    Authors:
    Krzysztof Bogdan, Michał Bosy, Tomasz Skalski
    Academic press:
    ALEA. Latin American Journal of Probability and Mathematical Statistics (rok: 2022, tom: 19, strony: 1045–1070), Wydawca: Inst. Mat. Pura Apl. (IMPA)
    Status:
    Published
    DOI:
    10.30757/ALEA.v19-43 - link to the publication
  7. On q-scale functions of spectrally negative Lévy processes
    Authors:
    Anita Behme, David Oechsler, René Schilling
    Academic press:
    Advances in Applied Probability (rok: 2023, tom: 55, strony: 56-84), Wydawca: Cambridge Univ. Press
    Status:
    Published
    DOI:
    10.1017/apr.2022.10 - link to the publication
  8. Anomalous diffusion limit for a kinetic equation with a thermostatted interface
    Authors:
    Krzysztof Bogdan, Tomasz Komorowski, Lorenzo Marino
    Academic press:
    Probability Theory and Related Fields (rok: 2023, tom: 46024, strony: 721-769), Wydawca: Springer-Verlag
    Status:
    Published
    DOI:
    10.1007/s00440-023-01251-3 - link to the publication
  9. Lévy processes, generalized moments and uniform integrability
    Authors:
    David Berger, Franziska Kühn, René Schilling
    Academic press:
    Probability and Mathematical Statistics (rok: 2022, tom: 42, strony: 109-131), Wydawca: Wrocław University of Science and Technology Publishing House
    Status:
    Published
    DOI:
    10.37190/0208-4147.00045 - link to the publication
  10. The Liouville theorem for a class of Fourier multipliers and its connection to coupling
    Authors:
    David Berger, René Schilling, Eugene Shargorodsky
    Academic press:
    Bulletin of the London Mathematical Society (rok: 2024, tom: 56, strony: 17), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1112/blms.13060 - link to the publication
  11. Second order elliptic partial differential equations driven by Levy white noise
    Authors:
    David Berger, Farid Mohamed
    Academic press:
    Modern Stochastics-Theory and Applications (rok: 2021, tom: 8, strony: 179-207), Wydawca: VteX
    Status:
    Published
    DOI:
    10.15559/21-VMSTA181 - link to the publication
  12. On weak solution of SDE driven by inhomogeneous singular Lévy noise
    Authors:
    Tadeusz Kulczycki, Alexei Kulik, Michał Ryznar
    Academic press:
    Transactions of the American Mathematical Society (rok: 2022, tom: 375 (7), strony: 4567-4618), Wydawca: AMS
    Status:
    Published
    DOI:
    10.1090/tran/8612 - link to the publication
  13. Relativistic stable operators with critical potentials
    Authors:
    Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski
    Academic press:
    Documenta Mathematica (rok: 2024, tom: 29, strony: 209–245), Wydawca: Deutsche Math. Ver. EMS Press
    Status:
    Published
    DOI:
    10.4171/DM/945 - link to the publication
  14. On the Liouville and strong Liouville properties for a class of non-local operators
    Authors:
    David Berger, René Schilling
    Academic press:
    Mathematica Scandinavica (rok: 2022, tom: 128, strony: 365-388), Wydawca: Mathematica Scandinavica
    Status:
    Published
    DOI:
    10.7146/math.scand.a-132068 - link to the publication
  15. Constructon and heat kernel estimates of general stable-like Markov processes
    Authors:
    Victoria Knopova, Alexei Kulik, René Schilling
    Academic press:
    Dissertationes Mathematicae (rok: 2021, tom: 569, strony: 86), Wydawca: Institute of Mathematics, Polish Academy of Sciences
    Status:
    Published
    DOI:
    10.4064/dm824-8-2021 - link to the publication
  16. Drift reduction method for SDEs driven by inhomogeneous singular Lévy noise
    Authors:
    Tadeusz Kulczycki, Oleksii Kulyk, Michał Ryznar
    Academic press:
    Bernoulli (rok: 2024, tom: 30, strony: 3089-3118), Wydawca: Bernoulli Society for Mathematical Statistics and Probability.
    Status:
    Published
    DOI:
    10.3150/23-BEJ1707 - link to the publication
  17. The fractional Laplacian with reflections
    Authors:
    Krzysztof Bogdan, Markus Kunze
    Academic press:
    Potential Analysis (rok: 2024, tom: 61, strony: 317–345), Wydawca: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s11118-023-10111-7 - link to the publication
  18. Quasi-infinite divisibility of a class of distributions with discrete part
    Authors:
    David Berger, Merve Kutlu
    Academic press:
    Proceedings of the American Mathematical Society (rok: 2023, tom: 151, strony: 2211-2224), Wydawca: AMS
    Status:
    Published
    DOI:
    10.1090/proc/16312 - link to the publication
  19. Sharp and plain estimates for Schrödinger perturbation of Gaussian kernel
    Authors:
    Tomasz Jakubowski, Karol Szczypkowski
    Academic press:
    Journal d'Analyse Mathématique (rok: 2024, tom: 162, strony: 255-282), Wydawca: Hebrew University Magnes Press
    Status:
    Published
    DOI:
    10.1007/s11854-023-0299-7 - link to the publication
  20. Subordinated Bessel heat kernels
    Authors:
    Krzysztof Bogdan, Konstantin Merz
    Academic press:
    Theory of Probability and Mathematical Statistics (rok: 2025, tom: 112, strony: 67-83), Wydawca: AMS
    Status:
    Published
    DOI:
    10.1090/tpms/1227 - link to the publication
  21. Small time chaos approximations of heat kernels of multidimensional diffusions
    Authors:
    Dmytro Ivanenko, Arturo Kohatsu-Higa, Alexi Kulik
    Academic press:
    BIT Numerical Mathematics (rok: 2023, tom: 63, strony: 34), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10543-023-00949-z - link to the publication
  22. Bound States and Heat Kernels for Fractional-Type Schrödinger Operators with Singular Potentials
    Authors:
    Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski
    Academic press:
    Communications in Mathematical Physics (rok: 2023, tom: 403, strony: 795–828), Wydawca: Springer-Verlag
    Status:
    Published
    DOI:
    10.1007/s00220-023-04810-w - link to the publication
  23. Caloric functions and boundary regularity for the fractional Laplacian in Lipschitz open sets
    Authors:
    Gavin Armstrong, Krzysztof Bogdan, Artur Rutkowski
    Academic press:
    Mathematische Annalen (rok: 2025, tom: 1, strony: 1199–1252), Wydawca: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s00208-024-02931-8 - link to the publication
  24. Non-symmetric Lévy-type operators
    Authors:
    Jakub Minecki, Karol Szczypkowski
    Academic press:
    Mathematische Nachrichten (rok: 2024, tom: 297, strony: 2234-2286), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1002/mana.202300150 - link to the publication
  25. Singular integrals of subordinators with applications to structural properties of SPDEs
    Authors:
    Changsong Deng, Lihu Xu, René Schilling
    Academic press:
    Transactions of the American Mathematical Society (rok: 2022, tom: 375, strony: 6043-6073), Wydawca: AMS
    Status:
    Published
    DOI:
    10.1090/tran/8595 - link to the publication

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