Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Regularity and asymptotics for multidimensional Markovian evolutions

2017/27/B/ST1/01339

Keywords:

jump-type Markov Process nonlocal operator Harnack inequality stationary measure excursions

Descriptors:

  • ST1_11: Partial differential equations
  • ST1_13: Probability and statistics

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 Bogdan 

Number of co-investigators in the project: 5

Call: OPUS 14 - announced on 2017-09-15

Amount awarded: 672 200 PLN

Project start date (Y-m-d): 2018-07-31

Project end date (Y-m-d): 2023-04-29

Project duration:: 57 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.

Equipment purchased [PL]

  1. Laptop (10 000 PLN)

Information in the final report

  • Publication in academic press/journals (13)
  1. Liouville's theorems for Lévy operators
    Authors:
    Tomasz Grzywny, Mateusz Kwaśnicki
    Academic press:
    Advances in Mathematics (rok: 2023, ), Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  2. Shot-down stable processes
    Authors:
    Krzysztof Bogdan, Kajetan Jastrzȩbski, Moritz Kassmann, Michał Kijaczko, Paweł Popławski
    Academic press:
    Studia Mathematica (rok: 2023, ), Wydawca: IM PAN
    Status:
    Submitted
    DOI:
    brak - link to the publication
  3. Heat kernels of non-local Schrödinger operators with Kato potentials
    Authors:
    Tomasz Grzywny, Kamil Kaleta, Paweł Sztonyk
    Academic press:
    Journal of Differential Equations (rok: 2022, tom: 340, strony: 273-308), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2022.08.038 - link to the publication
  4. Yaglom limit for unimodal Lévy processes
    Authors:
    Gavin Armstrong, Krzysztof Bogdan, Tomasz Grzywny, Łukasz Leżaj, Longmin Wang
    Academic press:
    Annales de l'Institut Henri Poincaré (rok: 2023, tom: 59, strony: 1688-1721), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1214/22-AIHP1301 - link to the publication
  5. Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels
    Authors:
    Krzysztof Bogdan, Konstantin Merz
    Academic press:
    Journal de Mathématiques Pures et Appliquées (rok: 2023, ), Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  6. Self-similar solution for fractional Laplacian in cones
    Authors:
    Krzysztof Bogdan, Piotr Knosalla, Łukasz Leżaj, Dominika Pilarczyk
    Academic press:
    Electronic Journal of Probability (rok: 2023, ), Wydawca: Institute of Mathematical Statistics
    Status:
    Submitted
    DOI:
    brak - link to the publication
  7. Optimal Hardy inequality for the fractional Laplacian on Lp
    Authors:
    K. Bogdan, T. Jakubowski, J. Lenczewska, K. Pietruska-Pałuba
    Academic press:
    Journal of Functional Analysis (rok: 2022, tom: 282(8), strony: Paper No. 109395, 31 pp), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2022.109395 - link to the publication
  8. Strong Feller property for SDEs driven by multiplicative cylindrical stable noise
    Authors:
    Michal Ryznar, Tadeusz Kulczycki, Paweł Sztonyk
    Academic press:
    Potential Analysis (rok: 2021, tom: 55, strony: 75-126), Wydawca: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s11118-020-09850-8 - link to the publication
  9. Burkholder inequality by Bregman divergence
    Authors:
    Krzysztof Bogdan, Mateusz Więcek
    Academic press:
    Bulletin of the Polish Academy of Sciences - Mathematics (rok: 2022, tom: 70, strony: 83-90), Wydawca: Publishing house of the Institute of Mathematics of the Polish Academy of Sciences
    Status:
    Published
    DOI:
    10.4064/ba220304-12-4 - link to the publication
  10. Self-similar solution for Hardy operator
    Authors:
    K. Bogdan, T. Jakubowski, P. Kim, D. Pilarczyk
    Academic press:
    Journal of Functional Analysis (rok: 2023, tom: 285, strony: 40), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2023.110014 - link to the publication
  11. The Douglas formula in Lp
    Authors:
    Krzysztof Bogdan, Damian Fafula and Artur Rutkowski
    Academic press:
    Nonlinear Differential Equations and Applications NoDEA (rok: 2023, tom: 30, strony: 22), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00030-023-00865-9 - link to the publication
  12. Positive harmonically bounded solutions for semi-linear equations
    Authors:
    Krzysztof Bogdan, Wolfhard Hansen
    Academic press:
    Journal of Differential Equations (rok: 2023, ), Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  13. Nonlinear nonlocal Douglas identity
    Authors:
    K. Bogdan, T. Grzywny, K. Pietruska-Pałuba, A. Rutkowski
    Academic press:
    Calculus of Variatons and Partal Differental Equations (rok: 2023, tom: 62, strony: 31), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00526-023-02458-x - link to the publication

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