Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

Delete all

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. 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
  2. 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
  3. 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
  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. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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

O Narodowym Centrum Nauki

Finansowanie nauki

Współpraca zagraniczna

Centrum prasowe

Deklaracja dostępności
Przetwarzanie danych osobowych
Polityka cookies

Partnerzy