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Properties of solutions of nonlocal equations

2015/17/B/ST1/01233

Keywords

Descriptors

  • ST1_13: Rachunek prawdopodobieństwa i statystyka matematyczna
  • ST1_11: Równania różniczkowe cząstkowe

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

Voivodeship: 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
2016-03-17
Project end date
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. Cost: 20 000 PLN

Information in the final report

Publication in academic press/journals (13)

  1. Strong Feller property for SDEs driven by multiplicative cylindrical stable noise

    Authors:
    Tadeusz Kulczycki, Michał Ryznar, Paweł Sztonyk
    Academic press:
    Potential Analysis (year: 2020, volume: -, pages: -), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-020-09850-8 – link to the publication

  2. Estimates of the transition densities or the reflected Brownian motion on simple nested fractals

    Authors:
    Mariusz Olszewski
    Academic press:
    Probability and Mathematical Statistics (year: 2019, volume: 39, pages: 423-440), Publisher: Wydawnictwo Uniwersytetu Wrocławskiego
    Status:
    Published
    DOI:
    10.19195/0208-4147.39.2.10 – link to the publication

  3. 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 (year: 2019, volume: 292(5), pages: 1008-1021), Publisher: Wiley
    Status:
    Published
    DOI:
    10.1002/mana.201700226 – link to the publication

  4. On functionals of excursions for Bessel processes of negative index

    Authors:
    Tomasz Byczkowski, Jacek Jakubowski, Maciej Wiśniewolski
    Academic press:
    Studia Mathematica (year: 2019, volume: 246, pages: 217-231), Publisher: Instytut Matematyczny Polskiej Akademii Nauk
    Status:
    Published
    DOI:
    10.4064/sm170309-15-3 – link to the publication

  5. Spatial asymptotics at infinity for heat kernels of integro-differential operators

    Authors:
    Kamil Kaleta, Paweł Sztonyk
    Academic press:
    Transactions of the American Mathematical Society (year: 2019, volume: 371, pages: 6627-6663), Publisher: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/tran/7538 – link to the publication

  6. Lifschitz tail for alloy-type models driven by the fractional Laplacian

    Authors:
    Kamil Kaleta, Katarzyna Pietruska-Pałuba
    Academic press:
    Journal of Functional Analysis (year: 2020, volume: 279(5), pages: 11689), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2020.108575 – link to the publication

  7. Typical long time behaviour of ground state-transformed jump processes

    Authors:
    Kamil Kaleta, József Lorinczi
    Academic press:
    Communications in Contemporary Mathematics (year: 2019, volume: -, pages: -), Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD
    Status:
    Published
    DOI:
    10.1142/S0219199719500020 – link to the publication

  8. Gradient estimates of Dirichlet heat kernels for unimodal Lévy processes

    Authors:
    Tadeusz Kulczycki, Michał Ryznar
    Academic press:
    Mathematische Nachrichten (year: 2018, volume: 291, pages: 374-397), Publisher: Wiley
    Status:
    Published
    DOI:
    10.1002/mana.201600443 – link to the publication

  9. 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 (year: 2018, volume: 15, pages: 1335–1375), Publisher: Instituto Nacional de Matematica Pura e Aplicada
    Status:
    Published
    DOI:
    10.30757/ALEA.v15-50 – link to the publication

  10. 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 (year: 2020, volume: 130(12), pages: 7185-7217), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2020.07.011 – link to the publication

  11. 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 (year: 2019, volume: 27(06), pages: -), Publisher: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0218348X19501044 – link to the publication

  12. Borell and Landau-Shepp inequalities for Cauchy-type measures

    Authors:
    Tomasz Byczkowski, Tomasz Żak
    Status:
    Accepted for publication

  13. Lifschitz tail for continuous Anderson models driven by Lévy operators

    Authors:
    Kamil Kaleta, Katarzyna Pietruska-Pałuba
    Status:
    Accepted for publication

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