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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Properties of solutions of nonlocal equations

2015/17/B/ST1/01233

Keywords:

stable processes Levy processes fractional Laplacian relativistic Hamiltonian generator of Levy process nonlocal equations nonlocal Anderson problem eigenfunctions harmonic functions

Descriptors:

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

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, Wydział Matematyki

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Tadeusz Kulczycki 

Number of co-investigators in the project: 4

Call: OPUS 9 - announced on 2015-03-16

Amount awarded: 459 200 PLN

Project start date (Y-m-d): 2016-03-17

Project end date (Y-m-d): 2019-09-16

Project duration:: 42 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 (20 000 PLN)

Information in the final report

  • Publication in academic press/journals (13)
  1. Transition density estimates for diagonal systems of SDEs driven by cylindrical α-stable processes
    Authors:
    Tadeusz Kulczycki, Michał Ryznar
    Academic press:
    ALEA-Latin American Journal of Probability and Mathematical Statistics (rok: 2018, tom: 15, strony: 1335–1375), Wydawca: Instituto Nacional de Matematica Pura e Aplicada
    Status:
    Published
    DOI:
    10.30757/ALEA.v15-50 - link to the publication
  2. Gradient estimates of Dirichlet heat kernels for unimodal Lévy processes
    Authors:
    Tadeusz Kulczycki, Michał Ryznar
    Academic press:
    Mathematische Nachrichten (rok: 2018, tom: 291, strony: 374-397), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1002/mana.201600443 - link to the publication
  3. On functionals of excursions for Bessel processes of negative index
    Authors:
    Tomasz Byczkowski, Jacek Jakubowski, Maciej Wiśniewolski
    Academic press:
    Studia Mathematica (rok: 2019, tom: 246, strony: 217-231), Wydawca: Instytut Matematyczny Polskiej Akademii Nauk
    Status:
    Published
    DOI:
    10.4064/sm170309-15-3 - link to the publication
  4. Typical long time behaviour of ground state-transformed jump processes
    Authors:
    Kamil Kaleta, József Lorinczi
    Academic press:
    Communications in Contemporary Mathematics (rok: 2019, tom: -, strony: -), Wydawca: WORLD SCIENTIFIC PUBL CO PTE LTD
    Status:
    Published
    DOI:
    10.1142/S0219199719500020 - link to the publication
  5. Starshape of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings
    Authors:
    Sven Jarohs, Tadeusz Kulczycki, Paolo Salani
    Academic press:
    Mathematische Nachrichten (rok: 2019, tom: 292(5), strony: 1008-1021), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1002/mana.201700226 - link to the publication
  6. Reflected Brownian motion on simple nested fractals
    Authors:
    Kamil Kaleta, Mariusz Olszewski, Katarzyna Pietruska-Pałuba
    Academic press:
    Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society (rok: 2019, tom: 27(06), strony: -), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0218348X19501044 - link to the publication
  7. Spatial asymptotics at infinity for heat kernels of integro-differential operators
    Authors:
    Kamil Kaleta, Paweł Sztonyk
    Academic press:
    Transactions of the American Mathematical Society (rok: 2019, tom: 371, strony: 6627-6663), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/tran/7538 - link to the publication
  8. Strong Feller property for SDEs driven by multiplicative cylindrical stable noise
    Authors:
    Tadeusz Kulczycki, Michał Ryznar, Paweł Sztonyk
    Academic press:
    Potential Analysis (rok: 2020, tom: -, strony: -), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-020-09850-8 - link to the publication
  9. Borell and Landau-Shepp inequalities for Cauchy-type measures
    Authors:
    Tomasz Byczkowski, Tomasz Żak
    Academic press:
    Probability and Mathematical Statistics , Wydawca: Wydawnictwo Uniwersytetu Wrocławskiego
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  10. Estimates of the transition densities or the reflected Brownian motion on simple nested fractals
    Authors:
    Mariusz Olszewski
    Academic press:
    Probability and Mathematical Statistics (rok: 2019, tom: 39, strony: 423-440), Wydawca: Wydawnictwo Uniwersytetu Wrocławskiego
    Status:
    Published
    DOI:
    10.19195/0208-4147.39.2.10 - link to the publication
  11. Lifschitz tail for alloy-type models driven by the fractional Laplacian
    Authors:
    Kamil Kaleta, Katarzyna Pietruska-Pałuba
    Academic press:
    Journal of Functional Analysis (rok: 2020, tom: 279(5), strony: 11689), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2020.108575 - link to the publication
  12. Semigroup properties of solutions of SDEs driven by Lévy processes with independent coordinates
    Authors:
    Tadeusz Kulczycki, Michał Ryznar
    Academic press:
    Stochastic Processes and their Applications (rok: 2020, tom: 130(12), strony: 7185-7217), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2020.07.011 - link to the publication
  13. Lifschitz tail for continuous Anderson models driven by Lévy operators
    Authors:
    Kamil Kaleta, Katarzyna Pietruska-Pałuba
    Academic press:
    Communications in Contemporary Mathematics , Wydawca: World Scientific Publishing
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication

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